質量維度一費米子

在理論物理學和宇宙學中，半自旋質量維度一費米子（mass dimension one fermions of spin one half）是暗物質的候選者。這些費米子與已知的物質粒子，如電子或中微子，有著根本的不同。儘管它們被有著半自旋，但它們並不是由著名的狄拉克體系描述的，而是由一種旋量克萊恩-戈登體系（spinorial Klein-Gordon formalism）描述的。

2004年，Dharam Vir Ahluwalia（IIT Guwahati）與Daniel Grumiller合作，提出了一個關於質量維度一半自旋費米子的意外理論發現

```
 Spin half fermions with mass dimension one: Theory, phenomenology, and dark matter,
 JCAP '''0507''' 012 (2005)
 [[doi:10.1088/1475-7516/2005/07/012]]
 [hep-th/0412080]</ref> 
```

```
 Dark matter: A Spin one half fermion field with mass dimension one?,
 Phys. Rev. D '''72''' ,067701 (2005)
 [[doi:10.1103/PhysRevD.72.067701]]
 [hep-th/0410192].</ref>。在随后的十年中，许多小组探索了新构造有趣的数学和物理性质，而D. V. Ahluwalia 和他的学生进一步完善了体系
```

```
 Elko and mass dimension one field of spin one half: causality and Fermi statistics,
 Int. J. Mod. Phys. D '''23''', no. 14, 1430026 (2015)
 [[doi:10.1142/S0218271814300262]]
 [arXiv:1502.01940 [hep-th]].</ref>
```

```
D. V. Ahluwalia and S. P. Horvath,
 Very special relativity as relativity of dark matter: The Elko connection,
 JHEP '''1011''', 078 (2010)
 [[doi:10.1007/JHEP11(2010)078]]
 [arXiv:1008.0436 [hep-ph]].</ref>
```

```
 Self-interacting Elko dark matter with an axis of locality,
 Phys. Rev. D '''83''', 065017 (2011)
 [[doi:10.1103/PhysRevD.83.065017]]
 [arXiv:0911.2947 [hep-ph]].</ref>
```

```
 Elko as self-interacting fermionic dark matter with axis of locality,
 Phys. Lett. B '''687''', 248 (2010)
 [[doi:10.1016/j.physletb.2010.03.010]]
 [arXiv:0804.1854 [hep-th]].</ref>
```

```
 Dynamical dispersion relation for ELKO dark spinor fields,
 Phys. Lett. B '''717''', 238 (2012)
 [[doi:10.1016/j.physletb.2012.09.004]]
 [arXiv:1203.1049 [hep-th]].</ref>
```

```
 Where are ELKO spinor fields in Lounesto spinor field classification?,
 Mod. Phys. Lett. A '''21''', (2006) 65
 [[doi:10.1142/S0217732306018482]]
 [math-ph/0506075].</ref>
```

```
 From Dirac spinor fields to ELKO,
 J. Math. Phys.  '''48''', 123517 (2007)
 [[doi:10.1063/1.2825840]]
 [arXiv:0711.1103 [math-ph]].</ref>
```

```
 Conformal Gravity with the most general ELKO Matter,
 Phys. Rev. D '''85''', 047502 (2012)
 [[doi:10.1103/PhysRevD.85.047502]]
 [arXiv:1101.2566 [gr-qc]].</ref>
```

```
 The most general ELKO Matter in torsional f(R)-theories,
 Annalen Phys.  '''524''', 77 (2012)
 [[doi:10.1002/andp.201100006]]
 [arXiv:1012.4282 [gr-qc]].</ref>
```

```
 The Most General Cosmological Dynamics for ELKO Matter Fields,
 Phys. Lett. B '''704''', 255 (2011)
 [[doi:10.1016/j.physletb.2011.09.024]]
 [arXiv:1011.1637 [gr-qc]].</ref><ref>K. E. Wunderle and R. Dick,
 A Supersymmetric Lagrangian for Fermionic Fields with Mass Dimension One,
 Can.  J.  Phys.  '''90''', 1185 (2012)
 [[doi:10.1139/p2012-075]]
 [arXiv:1010.0963 [hep-th]].</ref>
```

```
 Zero Energy of Plane-Waves for ELKOs,
 Gen. Rel. Grav.  '''43''', 1607 (2011)
 [[doi:10.1007/s10714-011-1143-4]]  [arXiv:1008.0334 [gr-qc]].</ref>
```

```
 Causality for ELKOs,
 Mod. Phys. Lett. A  '''25''', 2483 (2010)
 [[doi:10.1142/S0217732310033712]]
 [arXiv:0911.5304 [gr-qc]].</ref>
```

```
 ELKO, flagpole and flag-dipole spinor fields, and the instanton Hopf fibration,
 Adv.\ Appl.\ Clifford Algebras '''20''', 847 (2010)
 doi:10.1007/s00006-010-0225-9
 [arXiv:0811.2717 [math-ph]].</ref>。
```

因此，現在有了一個全新的自旋半費米子量子理論，它不存在上述所有問題。新費米子的相互作用不僅限於四維四次自相互作用，而且限於與希格斯粒子的四維耦合。新費米子與中微子的廣義Yukawa耦合提供了迄今為止未被懷疑的輕子數違反來源。因此，新的費米子為標準模型的狄拉克費米子提出了一個第一原則，暗物質夥伴與質量維度的對比，後者為三個半費米子與前者為一個半費米子，而沒有改變費米子到玻色子的統計數據。

質量維度一費米子自旋半場用Elko場作為其展開係數。Elko是最初德語 "Eigenspinoren des Ladungskonjugationsoperators"的縮寫，表示自旋體，它們是電荷共軛算符的本徵自旋體。由於新費米子的質量維數與標準模型物質場不匹配，他們被認為是暗物質的候選者。由於它們的類標量質量維數，它們與質量維數3/2狄拉克費米子有顯著差異

```
  ``Exploring Elko typical signature,''
 Phys. Lett. B '''706''', 352 (2012)
 [[doi:10.1016/j.physletb.2011.11.030]]
 [arXiv:1012.4642 [hep-ph]].
```

質量維度一費米子通過提供第一原理暗物質和暗能量場，對宇宙學有著意想不到的影響。2005年Ahluwalia-Grumiller 論文發表後，Christian Boehmer率先將Elko應用到宇宙學中，並認為Elko不僅是主要的暗物質候選者，也是宇宙膨脹的主要候選者

```
 The Einstein-Elko system: Can dark matter drive inflation?,''
 Annalen Phys.\  '''16''', 325 (2007),
 [[doi:10.1002/andp.200610237]]
 [gr-qc/0701087].</ref>。Einstein–Cartan–Elko系统由Boehmer首次引入宇宙学中。其他人已经证明，Elko也可以诱导一个时变的宇宙学常数<ref>C. G. Boehmer,
 The Einstein-Cartan-Elko system,
 Annalen Phys. '''16''', 38 (2007) 
 [[doi:10.1002/andp.200610216]]
 [gr-qc/0607088].</ref>。Abhishek Basak和同事们认为，快速滚动的宇宙膨胀吸引子点对于Elko来说是独一无二的，它独立于潜在的形式<ref name="#1">S.H. Pereira et al.
```

```
 [[doi:10.1088/1475-7516/2017/01/055]]
 [arXiv:1608.02777 [gr-qc]].</ref>
```

```
 Attractor behaviour in ELKO cosmology,
 JCAP  '''1304''', 025 (2013)
 [[doi:10.1088/1475-7516/2013/04/025]]
 [arXiv:1212.3445 [astro-ph.CO]].
```

Roldao da Roch研究了膜上的Elko局域化現象

```
 On coincidence problem and attractor solutions in ELKO dark energy model,
 Gen. Rel. Grav.'''44''', 2329 (2012)
 [[doi:10.1007/s10714-012-1392-x]]
 [arXiv:1109.1961 [gr-qc]].</ref> 
```

```
 Some remarks on the attractor behaviour in ELKO cosmology,
 JCAP '''1408''', 020 (2014)
 [[doi:10.1088/1475-7516/2014/08/020]]
 [arXiv:1402.6723 [gr-qc]].</ref>，并将其作为一种探索时空奇异拓扑特征的工具<ref>R. da Rocha, J. M. Hoff da Silva and A. E. Bernardini,
 Elko spinor fields as a tool for probing exotic topological spacetime features,
 Int. J. Mod. Phys. Conf. Ser.  '''3''', 133 (2011).
 [[doi:10.1142/S201019451100122X]]</ref>。
```

```
 Solutions to the problem of ELKO spinor localization in brane models,
 Phys.\ Rev.\ D '''91''', no. 8, 085008 (2015)
 [[doi:10.1103/PhysRevD.91.085008]]
 [arXiv:1411.6962 [hep-th]]</ref>
```

```
 Localization of 5D Elko Spinors on Minkowski Branes,
 Phys. Rev. D '''86''', 064012 (2012)
 [[doi:10.1103/PhysRevD.86.064012]]
 [arXiv:1107.2506 [hep-th]].</ref>
```

```
 Fermion localization mechanism with derivative geometrical coupling on branes,
 arXiv:1701.02429 [hep-th] https://arxiv.org/abs/1701.02429 .</ref>
```

```
 Super-inflation and generation of first order vector perturbations in ELKO,
 JCAP '''1505''', no. 05, 034 (2015)
 [[doi:10.1088/1475-7516/2015/05/034]]
 [arXiv:1410.5768 [hep-ph]].</ref>
```

```
 Inflation driven by dark spinor and Higgs fields,
 Int. J. Mod. Phys. D '''23''', no. 14, 1444006 (2014).
 [[doi:10.1142/S0218271814440064]]</ref>
```

```
 A new approach on the stability analysis in ELKO cosmology,
 Eur. Phys. J. C '''75''', no. 1, 36 (2015)
 [[doi:10.1140/epjc/s10052-015-3260-9]]
 [arXiv:1407.3401 [gr-qc]].</ref>
```

```
 ELKO fermions as dark matter candidates,
 Phys. Rev. D '''92''', 075027 (2015)
 [[doi:10.1103/PhysRevD.92.075027]]
 [arXiv:1407.0797 [hep-ph]].</ref>
```

```
 Exact solutions to Elko spinors in spatially flat Friedmann-Robertson-Walker spacetimes,
 JCAP '''1403''', 009 (2014)
 [[doi:10.1088/1475-7516/2014/03/009]]
 [arXiv:1401.3252 [hep-th]].</ref>
```

```
 ``Dark spinor model with torsion and cosmology,''
 Mod. Phys.  Lett. A  '''28''', 1350121 (2013)
 [[doi:10.1142/S0217732313501216]]
 [arXiv:1211.2981 [gr-qc]].</ref>
```

```
 Conformally-coupled dark spinor and FRW universe,
 Phys. Rev. D '''86''', 107301 (2012)
 [[doi:10.1103/PhysRevD.86.107301]]
 [arXiv:1206.2263 [gr-qc]].</ref>
```

```
 Dark spinor models in gravitation and cosmology,
 JHEP '''1007''', 053 (2010)
 [[doi:10.1007/JHEP07(2010)053]]
 [arXiv:1003.3858 [hep-th]].</ref>
```

```
 Spinor Dark Energy and Cosmological Coincidence Problem,
 Phys. Lett. B '''695''', 307 (2011)
 [[doi:10.1016/j.physletb.2010.10.053]]
 [arXiv:1002.4230 [gr-qc]].</ref><ref>C. G.~Boehmer and J. Burnett,
 Dark spinors with torsion in cosmology,
 Phys. Rev. D '''78''', 104001 (2008)
 [[doi:10.1103/PhysRevD.78.104001]]
 [arXiv:0809.0469 [gr-qc]].</ref>
```

```
 Modified scalar and tensor spectra in spinor driven inflation,
 JCAP '''1001''', 008 (2010)
 [[doi:10.1088/1475-7516/2010/01/008]]
 [arXiv:0807.3336 [astro-ph]].</ref>
```

```
 From inflation to recent cosmic acceleration: The Elko spinor field driving the evolution of the universe,
 arXiv:1702.07385 [gr-qc] https://arxiv.org/abs/1702.07385 .</ref>
```

```
 CMB Anisotropies and Inflation from Non-Standard Spinors,''
 Phys.  Lett.  B '''663''', 168 (2008)
 [[doi:10.1016/j.physletb.2008.04.008]]
 [arXiv:0710.2003 [astro-ph]].</ref>
```

```
 A Unified Model of Phantom Energy and Dark Matter,
 SIGMA '''4''', 009 (2008)
 [[doi:10.3842/SIGMA.2008.009]]
 [arXiv:0801.4728 [hep-th]].</ref>
```

```
 Dark spinor inflation: Theory primer and dynamics,
 Phys. Rev. D '''77''', 123535 (2008)
 [[doi:10.1103/PhysRevD.77.123535]]
 [arXiv:0804.0616 [astro-ph]].</ref>
```

```
 Dark spinors with torsion in cosmology,
 Phys. Rev. D '''78''', 104001 (2008)
 [[doi:10.1103/PhysRevD.78.104001]]
 [arXiv:0809.0469 [gr-qc]].</ref>
```

```
 Theory of neutral particles: McLennan-Case construct for neutrino, its generalization, and a fundamentally new wave equation,
 Int. J. Mod. Phys. A '''11''', 1855 (1996)
 [[doi:10.1142/S0217751X96000973]]
 [hep-th/9409134].</ref>
```

```
 Evidence for Majorana neutrinos: Dawn of a new era in space-time structure,
 hep-ph/0212222 https://arxiv.org/abs/hep-ph/0212222 .</ref>
```

```
 Extended set of Majorana spinors, a new dispersion relation, and a preferred frame,
 hep-ph/0305336 https://arxiv.org/abs/hep-ph/0305336 .</ref>
```

```
 Neutral particles in light of the Majorana-Ahluwalia ideas,
 Int. J. Theor. Phys.  '''34''', 2467 (1995)
 [[doi:10.1007/BF00670779]]
 [hep-th/9504158].</ref>
```

質量維度一費米子即使沒有宇宙學常數，也能通過量子效應誘導一個「宇宙學常數」項。這些導致非消失的效應可能是早期宇宙階段膨脹階段的原因。此外，對於較晚的演化，對應於具有時變宇宙學項的模型，這種量子效應與先前的最新研究一致

```
 [[doi:10.1088/1475-7516/2017/01/055]]
 [arXiv:1608.02777 [gr-qc]].
```