彈簧床墊推薦|彈簧床墊論壇

法捷耶夫-波波夫鬼粒子 維基百科，自由的百科全書 跳至導覽 跳至搜尋 在物理學中，法捷耶夫-波波夫鬼粒子（Faddeev–Popov ghost），是一種為了保持路徑積分表述的一致性而引入規範量子場論的附加場，以路德維希·法捷耶夫和維克多·波波夫的名字命名。[1] 目錄 1 費恩曼路徑積分表述的重複考慮 2 參見 3 參考 4 外部連結 費恩曼路徑積分表述的重複考慮 法捷耶夫-波波夫鬼粒子之所以是必須要引入的，是因為在路徑積分表述中，量子場論必須給出明確、非奇異的解，而由於規範對稱性的存在，我們無法從大量的因規範變換而相關的物理上等價的不同解挑選出唯一的解。這個問題起源於路徑積分重複考慮的規範對稱相關的場組態，這些其實對應於相同的物理態；路徑積分的測度包含一個係數，其不允許我們直接用一般的方法（例如費恩曼圖方法）從原始的作用量得到各種結果。但是，如果我們修改原始作用量，添加進去一個額外的場，打破規範對稱性，那麼一般方法就可以使用了。這種場就叫做鬼場。這一方法被稱作「法捷耶夫-波波夫方法」（見BRST量子化）。這種鬼場只是一種計算工具，對外部來說並不對應於任何一種實際粒子：鬼粒子在費恩曼圖中只作為虛粒子出現——或者說，只對應於某些規範組態的缺失。但是它對於維持么正性是至關重要的。 描述鬼粒子的公式和其具體形式與所選擇的具體規範有關，但對於所有規範得到的實際結果是相同的。費恩曼-胡夫特規範是用於這個目的時最簡單的規範，所以在這篇文章中我們都採用這種規範。

Faddeev–Popov ghost From Wikipedia, the free encyclopedia Jump to navigation Jump to search This article is about a specific type of ghost field. For ghosts in the general physics sense, see Ghosts (physics). Quantum field theory Feynmann Diagram Gluon Radiation.svg Feynman diagram History Background [show] Symmetries [show] Tools [show] Equations [show] Standard Model [show] Incomplete theories [show] Scientists [show] vte In physics, Faddeev–Popov ghosts (also called Faddeev–Popov gauge ghosts or Faddeev–Popov ghost fields) are extraneous fields which are introduced into gauge quantum field theories to maintain the consistency of the path integral formulation. They are named after Ludvig Faddeev and Victor Popov.[1][2] A more general meaning of the word ghost in theoretical physics is discussed in Ghost (physics). Contents 1 Overcounting in Feynman path integrals 1.1 Faddeev–Popov procedure 2 Spin–statistics relation violated 3 Gauge fields and associated ghost fields 4 Appearance in Feynman diagrams 5 Ghost field Lagrangian 6 References 7 External links Overcounting in Feynman path integrals The necessity for Faddeev–Popov ghosts follows from the requirement that quantum field theories yield unambiguous, non-singular solutions. This is not possible in the path integral formulation when a gauge symmetry is present since there is no procedure for selecting among physically equivalent solutions related by gauge transformation. The path integrals overcount field configurations corresponding to the same physical state; the measure of the path integrals contains a factor which does not allow obtaining various results directly from the action. Faddeev–Popov procedure Main article: BRST quantization It is possible, however, to modify the action, such that methods such as Feynman diagrams will be applicable by adding ghost fields which break the gauge symmetry. The ghost fields do not correspond to any real particles in external states: they appear as virtual particles in Feynman diagrams – or as the absence of gauge configurations. However, they are a necessary computational tool to preserve unitarity. The exact form or formulation of ghosts is dependent on the particular gauge chosen, although the same physical results must be obtained with all gauges since the gauge one chooses to carry out calculations is an arbitrary choice. The Feynman–'t Hooft gauge is usually the simplest gauge for this purpose, and is assumed for the rest of this article. Spin–statistics relation violated The Faddeev–Popov ghosts violate the spin–statistics relation, which is another reason why they are often regarded as "non-physical" particles. For example, in Yang–Mills theories (such as quantum chromodynamics) the ghosts are complex scalar fields (spin 0), but they anti-commute (like fermions). In general, anti-commuting ghosts are associated with fermionic symmetries, while commuting ghosts are associated with bosonic symmetries. Gauge fields and associated ghost fields Every gauge field has an associated ghost, and where the gauge field acquires a mass via the Higgs mechanism, the associated ghost field acquires the same mass (in the Feynman–'t Hooft gauge only, not true for other gauges). Appearance in Feynman diagrams In Feynman diagrams the ghosts appear as closed loops wholly composed of 3-vertices, attached to the rest of the diagram via a gauge particle at each 3-vertex. Their contribution to the S-matrix is exactly cancelled (in the Feynman–'t Hooft gauge) by a contribution from a similar loop of gauge particles with only 3-vertex couplings or gauge attachments to the rest of the diagram.[3] (A loop of gauge particles not wholly composed of 3-vertex couplings is not cancelled by ghosts.) The opposite sign of the contribution of the ghost and gauge loops is due to them having opposite fermionic/bosonic natures. (Closed fermion loops have an extra −1 associated with them; bosonic loops don't.) Ghost field Lagrangian The Lagrangian for the ghost fields c a ( x ) {\displaystyle c^{a}(x)\,} c^a(x)\, in Yang–Mills theories (where a {\displaystyle a} a is an index in the adjoint representation of the gauge group) is given by L ghost = ∂ μ c ¯ a ∂ μ c a + g f a b c ( ∂ μ c ¯ a ) A μ b c c . {\displaystyle {\mathcal {L}}_{\text{ghost}}=\partial _{\mu }{\bar {c}}^{a}\partial ^{\mu }c^{a}+gf^{abc}\left(\partial ^{\mu }{\bar {c}}^{a}\right)A_{\mu }^{b}c^{c}\;.} {\mathcal {L}}_{{{\text{ghost}}}}=\partial _{{\mu }}{\bar {c}}^{{a}}\partial ^{{\mu }}c^{{a}}+gf^{{abc}}\left(\partial ^{{\mu }}{\bar {c}}^{{a}}\right)A_{{\mu }}^{{b}}c^{{c}}\;. The first term is a kinetic term like for regular complex scalar fields, and the second term describes the interaction with the gauge fields as well as the Higgs field. Note that in abelian gauge theories (such as quantum electrodynamics) the ghosts do not have any effect since f a b c = 0 {\displaystyle f^{abc}=0} f^{abc} = 0 and, consequently, the ghost particles do not interact with the gauge fields.

如果我說你很喜歡唸義守，請把我的雙眼挖掉。

馬約拉納費米子 維基百科，自由的百科全書 (重新導向自 馬約拉納粒子) 跳至導覽 跳至搜尋 粒子物理學標準模型 Standard Model of Elementary Particles zh-hant.svg 背景顯示▼ 組成顯示▼ 組成顯示▼ 理論家顯示▼ 閱論編 馬約拉納費米子（英語：Majorana fermion）是一種費米子，它的反粒子就是它本身，1937年，埃托雷·馬約拉納發表論文假想這種粒子存在，因此而命名。與之相異，狄拉克費米子，指的是反粒子與自身不同的費米子。 除了微中子以外，所有標準模型的費米子的物理行為在低能量狀況與狄拉克費米子雷同（在電弱對稱性破壞後），但是微中子的本質尚未確定，微中子可能是狄拉克費米子或馬約拉納費米子。在凝聚體物理學裏，馬約拉納費米子以準粒子激發的形式存在於超導體裏，它可以用來形成具有非阿貝爾統計的馬約拉納束縛態。 目錄 1 理論 2 基本粒子 3 準粒子 4 超導實驗 5 參見 6 參考文獻 理論 這一概念由馬約拉納於1937年提出[1]，他對狄拉克方程式改寫得到了馬約拉納方程式，可以描述中性自旋1/2粒子，因而滿足這一方程式的粒子為自身的反粒子。 馬約拉納費米子與狄拉克費米子之間的區別可以用二次量子化的產生及湮沒算符表示。產生算符 γ j † {\displaystyle \gamma _{j}^{\dagger }} \gamma _{j}^{\dagger }會產生量子態為 j {\displaystyle j} j的費米子，湮沒算符 γ j {\displaystyle \gamma _{j}} \gamma _{j}則會將其湮沒（或者說產生對應的反粒子）。對於狄拉克費米子， γ j † {\displaystyle \gamma _{j}^{\dagger }} \gamma _{j}^{\dagger }與 γ j {\displaystyle \gamma _{j}} \gamma _{j}不同，而對於馬約拉納費米子，兩者相同。 埃托雷·馬約拉納在1937年假設存在馬約拉納費米子 基本粒子 目前的基本粒子中尚無已知的馬約拉納費米子。不過現在對於微中子的本質仍缺乏了解，它有可能是馬約拉納費米子或狄拉克費米子。無微中子雙β衰變可以視為一種雙β衰變事件，在這事件中，假若微中子確為馬約拉納費米子，則產生的兩個微中子會立刻相互湮沒，因為它們彼此都是對方的反粒子。[2]目前已有實驗在尋找這類衰變的蹤跡。[3] 在強子對撞機裏，無微中子雙β衰變過程的高能量類比是同正負號帶電輕子對的產生。[4]大型強子對撞機的超環面儀器與緊湊緲子線圈正在尋找這類事件。在手徵對稱性理論裏，這兩種過程之間存在著深厚的關連。[5]根據翹翹板機制，一種最為學術界接受的對於為甚麼微中子質量會如此微小的解釋，微中子是個天然的馬約拉納費米子。 馬約拉納費米子不能擁有電矩或磁矩，只能擁有環矩。[6]由於與電磁場的交互作用非常微小，它是冷暗物質的可能候選。[7]超對稱模型中假想的中性微子是馬約拉納費米子。 準粒子 在超導材料中馬約拉納費米子可作為準粒子產生。在超導體裏準粒子是自己的反粒子，因此使得這行為可以發生。超導體會規定電子-電洞對稱於準粒子激發，將能量為 E {\displaystyle E} E的產生算符 γ ( E ) {\displaystyle \gamma (E)} \gamma (E)與能量為 − E {\displaystyle -E} -E的湮沒算符 γ † ( − E ) {\displaystyle {\gamma ^{\dagger }(-E)}} {\gamma ^{\dagger }(-E)}關聯在一起。當能量（費米能級） E {\displaystyle E} E為零時，γ=γ†，馬約拉納費米子會束縛於某個缺陷，整個物體稱為「馬約拉納束縛態」或「馬約拉納零模」。[8]這術語比較合適，因為這些物體不再遵守費米統計，而是非阿貝爾統計（non-Abelian statistics）的任意子，變換次序會改變系統的狀態。馬約拉納束縛態所遵守的非阿貝爾統計使得它們有可能被應用於拓撲量子計算機。[9] 由於費米能階位於超導能隙中，因而出現中間能隙態（midgap state）。中間能隙態可能被俘獲於某些超導體或超流體的量子渦旋中，因此可能是馬約拉納費米子的發源處。[10][11][12]另外，超導線的端點或超導線缺陷處的肖克利態也可能是馬約拉納費米子的純電系發源處。[13]另外還可以用分數量子霍爾效應替代超導體為馬約拉納費米子的發源。[14] 2008年，傅亮與查爾斯·凱恩（Charles Kane）給出突破發展，他們預言馬約拉納束縛態會出現於拓撲絕緣體與超導體的介面。[15]隨後，其他物理學者發表了很多類似論文。 超導實驗 自傅亮等的論文發表後，許多科學家都試圖做實驗在超導體中尋找馬約拉納費米子。[16][17] 2012年物理學者發現了馬約拉納準粒子可能存在的首個證據[18][19]。來自荷蘭代爾夫特理工大學科維理奈米科學研究所的研究團隊進行了相關實驗[20]，他們將銻化銦奈米線與一條電路相連，一邊為正常的金電極接觸區域，另一邊為超導體薄片接觸區域。設備暴露於中等強度的磁場中，當施加在兩個電極間的電壓為0時導電率出現峰值，這與一對馬約拉納束縛態的形成相吻合，奈米線與超導體薄片接觸區域的兩端各有一個馬約拉納費米子。幾乎與此同時，由瑞典隆德大學以及美國普渡大學也各自獨立地在基於鈮和銻化銦約瑟夫森結結構中分別觀察到馬約拉納費米子所引起的零偏壓電導峰及交流分數約瑟夫森效應[21][22]。隨後，更多實驗室發現零偏壓電導峰現象，如以色列威爾茲曼研究所在砷化銦、丹麥波耳研究所在更為純淨的外延砷化銦-鋁系統中都發現了這種零能態。[23][24] 更多證據也在基於隧道掃描探針系統中被發現。2014年，普林斯頓大學研究團隊使用低溫掃描隧道顯微鏡發現在超導鉛元素板表面的一條鐵元素長鏈的兩端會出現零能電導峰。[25][26]未參與這項實驗的加州理工學院物理學者傑森·阿理夏（Jason Alicea）評論，這項實驗給出馬約拉納費米子存在的「令人信服」的證據，但是「我們應該注意到還有其他可能的解釋——即使暫時還沒有這樣的理論」。[27] 中國科學家在該領域也做出了傑出貢獻。2016年初，上海交通大學科研團隊在實驗室里成功地在超導拓撲薄膜系統中探測到了具有零能的漩渦態，並證明這種零能態具有安德烈夫反射自旋選擇性，這為馬約拉納零能態提供了另外一種準則，使實驗事實更加可靠。[28] 2017年，史丹福大學張首晟團隊與加州大學洛杉磯分校的王康隆團隊、加州大學歐文分校的夏晶團體合作，在超導-量子反常霍爾平台中發現了具有半個量子電導的邊緣電流，與理論預言的手性馬約拉納粒子十分吻合。這是在霍爾效應平台系統中第一個具有確鑿證據的馬約拉納測量結果。[29] 這些基於超導體平台的實驗可能證實了理論的馬約拉納零能束縛態。但是，具備零能態只是馬約拉納準粒子眾多性質中的一個，其它很多現象也可導致零能態。雖然零能態以及半個量子電導的越來越精確的測量可以排除大部分干擾因素，但是馬約拉納準粒子的證實必須找到更令人信服的證據，例如，非阿貝爾統計特性以及拓撲保護等。[26][27]

Majorana fermion From Wikipedia, the free encyclopedia Jump to navigation Jump to search Not to be confused with Majoron. Standard Model of particle physics Standard Model of Elementary Particles.svg Elementary particles of the Standard Model Background [show] Constituents [show] Limitations [show] Scientists [show] vte A Majorana fermion (/maɪəˈrɒnə ˈfɛərmiːɒn/[1]), also referred to as a Majorana particle, is a fermion that is its own antiparticle. They were hypothesized by Ettore Majorana in 1937. The term is sometimes used in opposition to a Dirac fermion, which describes fermions that are not their own antiparticles. With the exception of the neutrino, all of the Standard Model fermions are known to behave as Dirac fermions at low energy (after electroweak symmetry breaking), and none are Majorana fermions. The nature of the neutrinos is not settled—they may be either Dirac or Majorana fermions. In condensed matter physics, bound Majorana fermions can appear as quasiparticle excitations—the collective movement of several individual particles, not a single one, and they are governed by non-abelian statistics. Contents 1 Theory 1.1 Identities 2 Elementary particles 3 Majorana bound states 3.1 Experiments in superconductivity 3.2 Majorana bound states in quantum error correction 4 References 5 Further reading Theory The concept goes back to Majorana's suggestion in 1937[2] that neutral spin-​1⁄2 particles can be described by a real wave equation (the Majorana equation), and would therefore be identical to their antiparticle (because the wave functions of particle and antiparticle are related by complex conjugation). The difference between Majorana fermions and Dirac fermions can be expressed mathematically in terms of the creation and annihilation operators of second quantization: The creation operator γ j † {\displaystyle \gamma _{j}^{\dagger }} \gamma^{\dagger}_j creates a fermion in quantum state j {\displaystyle j} j (described by a real wave function), whereas the annihilation operator γ j {\displaystyle \gamma _{j}} \gamma_j annihilates it (or, equivalently, creates the corresponding antiparticle). For a Dirac fermion the operators γ j † {\displaystyle \gamma _{j}^{\dagger }} \gamma^{\dagger}_j and γ j {\displaystyle \gamma _{j}} \gamma_j are distinct, whereas for a Majorana fermion they are identical. The ordinary fermionic annihilation and creation operators f {\displaystyle f} f and f † {\displaystyle f^{\dagger }} {\displaystyle f^{\dagger }} can be written in terms of two Majorana operators γ 1 {\displaystyle \gamma _{1}} \gamma _{1} and γ 2 {\displaystyle \gamma _{2}} \gamma _{2} by f = ( γ 1 + i γ 2 ) / 2 , {\displaystyle f=(\gamma _{1}+i\gamma _{2})/{\sqrt {2}},} {\displaystyle f=(\gamma _{1}+i\gamma _{2})/{\sqrt {2}},} f † = ( γ 1 − i γ 2 ) / 2 . {\displaystyle f^{\dagger }=(\gamma _{1}-i\gamma _{2})/{\sqrt {2}}.} {\displaystyle f^{\dagger }=(\gamma _{1}-i\gamma _{2})/{\sqrt {2}}.} In supersymmetry models, neutralinos—superpartners of gauge bosons and Higgs bosons—are Majorana. Identities Another common convention for the normalization of the Majorana fermion operator is f = ( γ 1 + i γ 2 ) / 2 {\displaystyle f=(\gamma _{1}+i\gamma _{2})/2} {\displaystyle f=(\gamma _{1}+i\gamma _{2})/2} f † = ( γ 1 − i γ 2 ) / 2 {\displaystyle f^{\dagger }=(\gamma _{1}-i\gamma _{2})/2} {\displaystyle f^{\dagger }=(\gamma _{1}-i\gamma _{2})/2} This convention has the advantage that the Majorana operator squares to the identity. Using this convention, a collection of Majorana fermions γ i {\displaystyle \gamma _{i}} \gamma _{i} ( i = 1 , 2 , . . , n {\displaystyle i=1,2,..,n} {\displaystyle i=1,2,..,n}) obey the following commutation identities { γ i , γ j } = 2 δ i j {\displaystyle \{\gamma _{i},\gamma _{j}\}=2\delta _{ij}} {\displaystyle \{\gamma _{i},\gamma _{j}\}=2\delta _{ij}} ∑ i j k l [ γ i A i j γ j , γ k B k l γ l ] = ∑ i j 4 γ i [ A , B ] i j γ j {\displaystyle \sum _{ijkl}[\gamma _{i}A_{ij}\gamma _{j},\gamma _{k}B_{kl}\gamma _{l}]=\sum _{ij}4\gamma _{i}[A,B]_{ij}\gamma _{j}} {\displaystyle \sum _{ijkl}[\gamma _{i}A_{ij}\gamma _{j},\gamma _{k}B_{kl}\gamma _{l}]=\sum _{ij}4\gamma _{i}[A,B]_{ij}\gamma _{j}} where A {\displaystyle A} A and B {\displaystyle B} B are antisymmetric matrices. Elementary particles Because particles and antiparticles have opposite conserved charges, Majorana fermions have zero charge. All of the elementary fermions of the Standard Model have gauge charges, so they cannot have fundamental Majorana masses. However, the right-handed sterile neutrinos introduced to explain neutrino oscillation could have Majorana masses. If they do, then at low energy (after electroweak symmetry breaking), by the seesaw mechanism, the neutrino fields would naturally behave as six Majorana fields, with three of them expected to have very high masses (comparable to the GUT scale) and the other three expected to have very low masses (below 1 eV). If right-handed neutrinos exist but do not have a Majorana mass, the neutrinos would instead behave as three Dirac fermions and their antiparticles with masses coming directly from the Higgs interaction, like the other Standard Model fermions. Ettore Majorana hypothesised the existence of Majorana fermions in 1937 The seesaw mechanism is appealing because it would naturally explain why the observed neutrino masses are so small. However, if the neutrinos are Majorana then they violate the conservation of lepton number and even of B − L. Neutrinoless double beta decay has not (yet) been observed,[3] but if it does exist, it can be viewed as two ordinary beta decay events whose resultant antineutrinos immediately annihilate with each other, and is only possible if neutrinos are their own antiparticles.[4] The high-energy analog of the neutrinoless double beta decay process is the production of same-sign charged lepton pairs in hadron colliders;[5] it is being searched for by both the ATLAS and CMS experiments at the Large Hadron Collider. In theories based on left–right symmetry, there is a deep connection between these processes.[6] In the currently most-favored explanation of the smallness of neutrino mass, the seesaw mechanism, the neutrino is “naturally” a Majorana fermion. Majorana fermions cannot possess intrinsic electric or magnetic moments, only toroidal moments.[7][8][9] Such minimal interaction with electromagnetic fields makes them potential candidates for cold dark matter.[10][11] Majorana bound states In superconducting materials, Majorana fermions can emerge as (non-fundamental) quasiparticles (more commonly referred to as Bogoliubov quasiparticles in condensed matter physics). This becomes possible because a quasiparticle in a superconductor is its own antiparticle. Mathematically, the superconductor imposes electron hole "symmetry" on the quasiparticle excitations, relating the creation operator γ ( E ) {\displaystyle \gamma (E)} \gamma(E) at energy E {\displaystyle E} E to the annihilation operator γ † ( − E ) {\displaystyle {\gamma ^{\dagger }(-E)}} {\gamma^{\dagger}(-E)} at energy − E {\displaystyle -E} -E. Majorana fermions can be bound to a defect at zero energy, and then the combined objects are called Majorana bound states or Majorana zero modes.[12] This name is more appropriate than Majorana fermion (although the distinction is not always made in the literature), because the statistics of these objects is no longer fermionic. Instead, the Majorana bound states are an example of non-abelian anyons: interchanging them changes the state of the system in a way that depends only on the order in which the exchange was performed. The non-abelian statistics that Majorana bound states possess allows them to be used as a building block for a topological quantum computer.[13] A quantum vortex in certain superconductors or superfluids can trap midgap states, so this is one source of Majorana bound states.[14][15][16] Shockley states at the end points of superconducting wires or line defects are an alternative, purely electrical, source.[17] An altogether different source uses the fractional quantum Hall effect as a substitute for the superconductor.[18] Experiments in superconductivity In 2008, Fu and Kane provided a groundbreaking development by theoretically predicting that Majorana bound states can appear at the interface between topological insulators and superconductors.[19][20] Many proposals of a similar spirit soon followed, where it was shown that Majorana bound states can appear even without any topological insulator. An intense search to provide experimental evidence of Majorana bound states in superconductors[21][22] first produced some positive results in 2012.[23][24] A team from the Kavli Institute of Nanoscience at Delft University of Technology in the Netherlands reported an experiment involving indium antimonide nanowires connected to a circuit with a gold contact at one end and a slice of superconductor at the other. When exposed to a moderately strong magnetic field the apparatus showed a peak electrical conductance at zero voltage that is consistent with the formation of a pair of Majorana bound states, one at either end of the region of the nanowire in contact with the superconductor.[25]. Simultaneously, a group from Purdue University and University of Notre Dame reported observation of fractional Josephson effect (decrease of the Josephson frequency by a factor of 2) in indium antimonide nanowires connected to two superconducting contacts and subjected to a moderate magnetic field[26], another signature of Majorana bound states[27]. Bound state with zero energy was soon detected by several other groups in similar hybrid devices,[28][29][30][31], and fractional Josephson effect was observed in topological insulator HgTe with superconducting contacts[32] The aforementioned experiments marks a possible verification of independent 2010 theoretical proposals from two groups[33][34] predicting the solid state manifestation of Majorana bound states in semiconducting wires. However, it was also pointed out that some other trivial non-topological bounded states[35] could highly mimic the zero voltage conductance peak of Majorana bound state. The subtle relation between those trivial bound states and Majorana bound states was reported by the researchers in Niels Bohr Institute,[36] who can directly "watch" coalescing Andreev bound states evolving into Majorana bound states, thanks to a much cleaner semiconductor-superconductor hybrid system. In 2014, evidence of Majorana bound states was also observed using a low-temperature scanning tunneling microscope, by scientists at Princeton University.[37][38] It was suggested that Majorana bound states appeared at the edges of a chain of iron atoms formed on the surface of superconducting lead. The detection was not decisive because of possible alternative explanations.[39] Majorana fermions may also emerge as quasiparticles in quantum spin liquids, and were observed by researchers at Oak Ridge National Laboratory, working in collaboration with Max Planck Institute and University of Cambridge on 4 April 2016.[40][41] Chiral Majorana fermions were detected in 2017, in a quantum anomalous Hall effect/superconductor hybrid device.[42][43] In this system, Majorana fermions edge mode will give a rise to a 1 2 e 2 h {\displaystyle {\frac {1}{2}}{\frac {e^{2}}{h}}} {\displaystyle {\frac {1}{2}}{\frac {e^{2}}{h}}} conductance edge current. On 16 August 2018, a strong evidence for the existence of Majorana bound states (or Majorana anyons) in an iron-based superconductor, which many alternative trivial explanations cannot account for, was reported by researchers in Prof. Gao Hong-jun's team and Prof. Ding Hong's team at Institute of Physics, Chinese Academy of Sciences and University of Chinese Academy of Sciences, when they used scanning tunneling spectroscopy on the superconducting Dirac surface state of the iron-based superconductor. It was the first time that Majorana particles were observed in a bulk of pure substance.[44] Majorana bound states in quantum error correction Majorana bound states can also be realized in quantum error correcting codes. This is done by creating so called 'twist defects' in codes such as the Toric code[45] which carry unpaired Majorana modes.[46] The braiding of Majoranas realized in such a way forms a projective representation of the braid group.[47] Such a realization of Majoranas would allow them to be used to store and process quantum information within a quantum computation.[48] Though the codes typically have no Hamiltonian to provide suppression of errors, fault-tolerance would be provided by the underlying quantum error correcting code.

怎惹?

https://en.wikipedia.org/wiki/Sfermion

大亞灣核反應爐微中子實驗 2016年2月，大亞灣核反應爐微中子實驗團隊發表論文表示，收集到的反電微中子，其數量比理論預測低6%。這結果意味著有些反電微中子可能已變換成無法探測到的輕質量惰性微中子。[2][3]

Sterile neutrino From Wikipedia, the free encyclopedia Jump to navigation Jump to search Sterile neutrino, right-handed neutrinoComposition Elementary particle Statistics Fermionic Generation unknown Interactions gravity; other potential unknown interactions Status Hypothetical Types unknown Mass unknown Electric charge 0 Color charge none Spin ​1⁄2 Spin states 2 Weak isospin projection 0 Weak hypercharge 0 Chirality right handed B − L depends on L charge assignment X −5 Sterile neutrinos (or inert neutrinos) are hypothetical particles[1] (neutral leptons – neutrinos) that interact only via gravity and do not interact via any of the fundamental interactions of the Standard Model. The term sterile neutrino is used to distinguish them from the known active neutrinos in the Standard Model, which are charged under the weak interaction. This term usually refers to neutrinos with right-handed chirality (see right-handed neutrino), which may be added to the Standard Model. Occasionally it is used in a general sense for any neutral fermion, instead of the more cautiously vague name neutral heavy leptons (NHLs) or heavy neutral leptons (HNLs). The existence of right-handed neutrinos is theoretically well-motivated, as all other known fermions have been observed with both left and right chirality, and they can explain the observed active neutrino masses in a natural way. The mass of the right-handed neutrinos themselves is unknown and could have any value between 1015 GeV and less than 1 eV.[2] The number of sterile neutrino types (should they exist) is not yet theoretically established. This is in contrast to the number of active neutrino types, which has to equal that of charged leptons and quark generations to ensure the anomaly freedom of the electroweak interaction. The search for sterile neutrinos is an active area of particle physics. If they exist and their mass is smaller than the energies of particles in the experiment, they can be produced in the laboratory, either by mixing between active and sterile neutrinos or in high energy particle collisions. If they are heavier, the only directly observable consequence of their existence would be the observed active neutrino masses. They may, however, be responsible for a number of unexplained phenomena in physical cosmology and astrophysics, including dark matter, baryogenesis or dark radiation.[2] In May 2018, physicists of the MiniBooNE experiment reported a stronger neutrino oscillation signal than expected, a possible hint of sterile neutrinos.[3][4] Contents 1 Motivation 2 Properties 2.1 Mass 2.2 Dirac and Majorana terms 2.3 Seesaw mechanism 3 Detection attempts 4 See also 5 Notes 6 References 7 External links Motivation See also: Neutrino: Chirality and Neutrino oscillation Experimental results show that all produced and observed neutrinos have left-handed helicities (spin antiparallel to momentum), and all antineutrinos have right-handed helicities, within the margin of error. In the massless limit, it means that only one of two possible chiralities is observed for either particle. These are the only helicities (and chiralities) included in the Standard Model of particle interactions. Recent experiments such as neutrino oscillation, however, have shown that neutrinos have a non-zero mass, which is not predicted by the Standard Model and suggests new, unknown physics. This unexpected mass explains neutrinos with right-handed helicity and antineutrinos with left-handed helicity: Since they do not move at the speed of light, their helicity is not relativistic invariant (it is possible to move faster than them and observe the opposite helicity). Yet all neutrinos have been observed with left-handed chirality, and all antineutrinos right-handed. Chirality is a fundamental property of particles and is relativistic invariant: It is the same regardless of the particle's speed and mass in every inertial reference frame. Although note that a particle with mass that starts out left-handed can develop a right-handed component as it travels – chirality is not conserved in the propagation of a free particle. The question, thus, remains: Do neutrinos and antineutrinos differ only in their chirality? Or do exotic right-handed neutrinos and left-handed antineutrinos exist as separate particles from the common left-handed neutrinos and right-handed antineutrinos? Properties Such particles would belong to a singlet representation with respect to the strong interaction and the weak interaction, having zero electric charge, zero weak hypercharge, zero weak isospin, and, as with the other leptons, no color, although they do have a B-L of −1. If the standard model is embedded in a hypothetical SO(10) grand unified theory, they can be assigned an X charge of −5. The left-handed anti-neutrino has a B-L of +1 and an X charge of +5. Due to the lack of electric charge, hypercharge, and color, sterile neutrinos would not interact electromagnetically, weakly, or strongly, making them extremely difficult to detect. They have Yukawa interactions with ordinary leptons and Higgs bosons, which via the Higgs mechanism lead to mixing with ordinary neutrinos. In experiments involving energies larger than their mass they would participate in all processes in which ordinary neutrinos take part, but with a quantum mechanical probability that is suppressed by the small mixing angle. That makes it possible to produce them in experiments if they are light enough. They would also interact gravitationally due to their mass, and if they are heavy enough, could explain cold dark matter or warm dark matter. In some grand unification theories, such as SO(10), they also interact via gauge interactions which are extremely suppressed at ordinary energies because their gauge boson is extremely massive. They do not appear at all in some other GUTs, such as the Georgi–Glashow model (i.e. all its SU(5) charges or quantum numbers are zero). Mass All particles are initially massless under the Standard Model, since there are no Dirac mass terms in the Standard Model's Lagrangian. The only mass terms are generated by the Higgs mechanism, which produces non-zero Yukawa couplings between the left-handed components of fermions, the Higgs field, and their right-handed components. This occurs when the SU(2) doublet Higgs field ϕ {\displaystyle \phi } \phi acquires its non-zero vacuum expectation value, ν {\displaystyle \nu } \nu , spontaneously breaking its SU(2)L × U(1) symmetry, and thus yielding non-zero Yukawa couplings: L ( ψ ) = ψ ¯ ( i ∂ / ) ψ − G ψ ¯ L ϕ ψ R {\displaystyle {\mathcal {L}}(\psi )={\bar {\psi }}(i\partial \!\!\!/)\psi -G{\bar {\psi }}_{L}\phi \psi _{R}} {\mathcal {L}}(\psi )={\bar {\psi }}(i\partial \!\!\!/)\psi -G{\bar \psi }_{L}\phi \psi _{R} Such is the case for charged leptons, like the electron; but within the standard model, the right-handed neutrino does not exist, so even with a Yukawa coupling neutrinos remain massless. In other words, there are no mass terms for neutrinos under the Standard Model: the model only contains a left-handed neutrino and its antiparticle, a right-handed antineutrino, for each generation, produced in weak eigenstates during weak interactions. (See neutrino masses in the Standard Model for a detailed explanation.) In the seesaw mechanism, one eigenvector of the neutrino mass matrix, which includes sterile neutrinos, is predicted to be significantly heavier than the other. A sterile neutrino would have the same weak hypercharge, weak isospin, and mass as its antiparticle. For any charged particle, for example the electron, this is not the case: its antiparticle, the positron, has opposite electric charge, among other opposite charges. Similarly, an up quark has a charge of +​ 2⁄3 and (for example) a color charge of red, while its antiparticle has an electric charge of −​ 2⁄3 and a color charge of anti-red. Dirac and Majorana terms Sterile neutrinos allow the introduction of a Dirac mass term as usual. This can yield the observed neutrino mass, but it requires that the strength of the Yukawa coupling be much weaker for the electron neutrino than the electron, without explanation. Similar problems (although less severe) are observed in the quark sector, where the top and bottom masses differ by a factor of 40. Unlike for the left-handed neutrino, a Majorana mass term can be added for a sterile neutrino without violating local symmetries (weak isospin and weak hypercharge) since it has no weak charge. However, this would still violate total lepton number. It is possible to include both Dirac and Majorana terms: this is done in the seesaw mechanism (below). In addition to satisfying the Majorana equation, if the neutrino were also its own antiparticle, then it would be the first Majorana fermion. In that case, it could annihilate with another neutrino, allowing neutrinoless double beta decay. The other case is that it is a Dirac fermion, which is not its own antiparticle. To put this in mathematical terms, we have to make use of the transformation properties of particles. For free fields, a Majorana field is defined as an eigenstate of charge conjugation. However, neutrinos interact only via the weak interactions, which are not invariant under charge conjugation (C), so an interacting Majorana neutrino cannot be an eigenstate of C. The generalized definition is: "a Majorana neutrino field is an eigenstate of the CP transformation". Consequently, Majorana and Dirac neutrinos would behave differently under CP transformations (actually Lorentz and CPT transformations). Also, a massive Dirac neutrino would have nonzero magnetic and electric dipole moments, whereas a Majorana neutrino would not. However, the Majorana and Dirac neutrinos are different only if their rest mass is not zero. For Dirac neutrinos, the dipole moments are proportional to mass and would vanish for a massless particle. Both Majorana and Dirac mass terms however can appear in the mass Lagrangian. Seesaw mechanism Main article: Seesaw mechanism In addition to the left-handed neutrino, which couples to its family charged lepton in weak charged currents, if there is also a right-handed sterile neutrino partner (a weak isosinglet with zero charge) then it is possible to add a Majorana mass term without violating electroweak symmetry. Both neutrinos have mass and handedness is no longer preserved (thus "left or right-handed neutrino" means that the state is mostly left or right-handed). To get the neutrino mass eigenstates, we have to diagonalize the general mass matrix M ν {\displaystyle M_{\nu }} {\displaystyle M_{\nu }}: M ν = ( 0 m D m D M N H L ) {\displaystyle M_{\nu }={\begin{pmatrix}0&m_{D}\\m_{D}&M_{NHL}\end{pmatrix}}} {\displaystyle M_{\nu }={\begin{pmatrix}0&m_{D}\\m_{D}&M_{NHL}\end{pmatrix}}} where M N H L {\displaystyle M_{NHL}} M_{{NHL}} is big and m D {\displaystyle m_{D}} m_{D} is of intermediate size terms. Apart from empirical evidence, there is also a theoretical justification for the seesaw mechanism in various extensions to the Standard Model. Both Grand Unification Theories (GUTs) and left-right symmetrical models predict the following relation: m ν ≪ m D ≪ M N H L {\displaystyle m_{\nu }\ll m_{D}\ll M_{NHL}} {\displaystyle m_{\nu }\ll m_{D}\ll M_{NHL}} According to GUTs and left-right models, the right-handed neutrino is extremely heavy: M N H L ≈ {\textstyle M_{NHL}\approx } {\textstyle M_{NHL}\approx } 105 to 1012 GeV, while the smaller eigenvalue is approximately equal to m ν ≈ m D 2 M N H L {\displaystyle m_{\nu }\approx {\frac {m_{D}^{2}}{M_{NHL}}}} m_{{\nu }}\approx {\frac {m_{D}^{2}}{M_{{NHL}}}} This is the seesaw mechanism: as the sterile right-handed neutrino gets heavier, the normal left-handed neutrino gets lighter. The left-handed neutrino is a mixture of two Majorana neutrinos, and this mixing process is how sterile neutrino mass is generated. Detection attempts The production and decay of sterile neutrinos could happen through the mixing with virtual ("off mass shell") neutrinos. There were several experiments set up to discover or observe NHLs, for example the NuTeV (E815) experiment at Fermilab or LEP-l3 at CERN. They all led to establishing limits to observation, rather than actual observation of those particles. If they are indeed a constituent of dark matter, sensitive X-ray detectors would be needed to observe the radiation emitted by their decays.[5] Sterile neutrinos may mix with ordinary neutrinos via a Dirac mass after electroweak symmetry breaking, in analogy to quarks and charged leptons.[citation needed] Sterile neutrinos and (in more-complicated models) ordinary neutrinos may also have Majorana masses. In the type 1 seesaw mechanism both Dirac and Majorana masses are used to drive ordinary neutrino masses down and make the sterile neutrinos much heavier than the Standard Model's interacting neutrinos. In some models[which?] the heavy neutrinos can be as heavy as the GUT scale (≈1015 GeV). In other models[which?] they could be lighter than the weak gauge bosons W and Z as in the so-called νMSM model where their masses are between GeV and keV. A light (with the mass ≈1 eV) sterile neutrino was suggested as a possible explanation of the results of the Liquid Scintillator Neutrino Detector experiment. On 11 April 2007, researchers at the MiniBooNE experiment at Fermilab announced that they had not found any evidence supporting the existence of such a sterile neutrino.[6] More-recent results and analysis have provided some support for the existence of the sterile neutrino.[7][8] Two separate detectors near a nuclear reactor in France found 3% of anti-neutrinos missing. They suggested the existence of a fourth neutrino with a mass of 1.2 eV.[9] Sterile neutrinos are also candidates for dark radiation. Daya Bay has also searched for a light sterile neutrino and excluded some mass regions.[10] Daya Bay Collaboration measured the anti-neutrino energy spectrum, and found that anti-neutrinos at an energy of around 5 MeV are in excess relative to theoretical expectations. It also recorded 6% missing anti-neutrinos.[11] This could suggest that sterile neutrinos exist or that our understanding of neutrinos is not complete. The number of neutrinos and the masses of the particles can have large-scale effects that shape the appearance of the cosmic microwave background. The total number of neutrino species, for instance, affects the rate at which the cosmos expanded in its earliest epochs: more neutrinos means a faster expansion. The Planck Satellite 2013 data release is compatible with the existence of a sterile neutrino. The implied mass range is from 0–3 eV.[12][not in citation given (See discussion.)] In 2016, scientists at the IceCube Neutrino Observatory did not find any evidence for the sterile neutrino.[13] However, in May 2018, physicists of the MiniBooNE experiment reported a stronger neutrino oscillation signal than expected, a possible hint of sterile neutrinos.[3][4] See also MiniBooNE at Fermilab

2014年的新發現 在英國萊斯特大學的研究小組利用歐洲航天局X射線天文台和XMM-牛頓天文台整個資料庫的研究中的發現了直接檢測到暗物質的潛在暗示。在X射線背景即移除了明亮X射線光源後的天空中發現了一個季節性信號，與軸子的理論預測相一致。軸子可能產生於太陽核心，在地球磁場作用下轉化為X射線，據預測通過磁場朝太陽方向觀察時，軸子產生的X射線信號將最強烈，這與觀測相吻合。[5] https://en.wikipedia.org/wiki/Axion