质量维度一费米子

在理论物理学和宇宙学中，半自旋质量维度一费米子（mass dimension one fermions of spin one half）是暗物质的候选者。这些费米子与已知的物质粒子，如电子或中微子，有着根本的不同。尽管它们被有着半自旋，但它们并不是由著名的狄拉克体系描述的，而是由一种旋量克莱恩-戈登体系（spinorial Klein-Gordon formalism）描述的。

2004年，Dharam Vir Ahluwalia（IIT Guwahati）与Daniel Grumiller合作，提出了一个关于质量维度一半自旋费米子的意外理论发现
D. V. Ahluwalia and D. Grumiller,
  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] 
D. V. Ahluwalia and D. Grumiller,
  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].。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
D. V. Ahluwalia and A. C. Nayak,
  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]].
 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]].
D. V. Ahluwalia, C. Y. Lee and D. Schritt,
  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]].
D. V. Ahluwalia, C. Y. Lee and D. Schritt,
  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]].
A. E. Bernardini and R. da Rocha,
  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]].
R. da Rocha and W. A. Rodrigues, Jr.,
  Where are ELKO spinor fields in Lounesto spinor field classification?,
  Mod. Phys. Lett. A 21, (2006) 65
  doi:10.1142/S0217732306018482
  [math-ph/0506075].
R. da Rocha and J. M. Hoff da Silva,
  From Dirac spinor fields to ELKO,
  J. Math. Phys.  48, 123517 (2007)
  doi:10.1063/1.2825840
  [arXiv:0711.1103 [math-ph]].
L. Fabbri,
  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]].
L. Fabbri and S. Vignolo,
  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]].
L. Fabbri,
  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]].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]].
L. Fabbri,
  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]].
L. Fabbri,
  Causality for ELKOs,
  Mod. Phys. Lett. A  25, 2483 (2010)
  doi:10.1142/S0217732310033712
  [arXiv:0911.5304 [gr-qc]].
R. da Rocha and J. M. Hoff da Silva,
  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]].。

然而，体系有两个令人不安的特点，即非局域性和对洛伦兹对称的微妙破坏。这两个问题的起源现在被追溯到一个隐藏的自由定义，旋量和伴随的关联场D. V. Ahluwalia, The theory of local mass dimension one fermions of spin one half,  Adv. Appl. Clifford Algebras 27 (2017) no.3, 2247-2285 . doi:10.1007/s00006-017-0775-1。因此，现在有了一个全新的自旋半费米子量子理论，它不存在上述所有问题。新费米子的相互作用不仅限于四维四次自相互作用，而且限于与希格斯粒子的四维耦合。新费米子与中微子的广义Yukawa耦合提供了迄今为止未被怀疑的轻子数违反来源。因此，新的费米子为标准模型的狄拉克费米子提出了一个第一原则，暗物质伙伴与质量维度的对比，后者为三个半费米子与前者为一个半费米子，而没有改变费米子到玻色子的统计数据。

质量维度一费米子自旋半场用Elko场作为其展开系数。Elko是最初德语 "Eigenspinoren des Ladungskonjugationsoperators"的缩写，表示自旋体，它们是电荷共轭算符的本征自旋体。由于新费米子的质量维数与标准模型物质场不匹配，他们被认为是暗物质的候选者。由于它们的类标量质量维数，它们与质量维数3/2狄拉克费米子有显著差异M. Dias, F. de Campos and J. M. Hoff da Silva,
   ``Exploring Elko typical signature,''
  Phys. Lett. B 706, 352 (2012)
  doi:10.1016/j.physletb.2011.11.030
  [arXiv:1012.4642 [hep-ph]].。

质量维度一费米子通过提供第一原理暗物质和暗能量场，对宇宙学有着意想不到的影响。2005年Ahluwalia-Grumiller 论文发表后，Christian Boehmer率先将Elko应用到宇宙学中，并认为Elko不仅是主要的暗物质候选者，也是宇宙膨胀的主要候选者C.G.Boehmer,
  The Einstein-Elko system: Can dark matter drive inflation?,''
  Annalen Phys.\  16, 325 (2007),
  doi:10.1002/andp.200610237
  [gr-qc/0701087].。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C. G. Boehmer,
  The Einstein-Cartan-Elko system,
  Annalen Phys. 16, 38 (2007) 
  doi:10.1002/andp.200610216
  [gr-qc/0607088].。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S.H. Pereira et al.
Λ(t) cosmology induced by a slowly varying Elko field, JCAP 1701, no. 01, 055 (2017)
  doi:10.1088/1475-7516/2017/01/055
  [arXiv:1608.02777 [gr-qc]].
A. Basak, J. R. Bhatt, S. Shankaranarayanan and K. V. Prasantha Varma,
  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局域化现象H. M. Sadjadi,
  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]]. 
S. H. Pereira, A. Pinho S.S. and J. M. Hoff da Silva,
  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]].，并将其作为一种探索时空奇异拓扑特征的工具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。

以下参考文献作为Elko场和质量维度一费米子的参考
I. C. Jardim, G. Alencar, R. R. Landim and R. N. Costa Filho,
  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]]
Y. X. Liu, X. N. Zhou, K. Yang and F. W. Chen,
  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]].
Y. Y. Li, Y. P. Zhang, W. D. Guo and Y. X. Liu,
  Fermion localization mechanism with derivative geometrical coupling on branes,
  arXiv:1701.02429 [hep-th] https://arxiv.org/abs/1701.02429 .

A. Basak and S. Shankaranarayanan,
  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]].
J. Lee, T. H. Lee and P. Oh,
  Inflation driven by dark spinor and Higgs fields,
  Int. J. Mod. Phys. D 23, no. 14, 1444006 (2014).
  doi:10.1142/S0218271814440064
A. Pinho S. S., S. H. Pereira and J. F. Jesus,
  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]].
B. Agarwal, P. Jain, S. Mitra, A. C. Nayak and R. K. Verma,
  ELKO fermions as dark matter candidates,
  Phys. Rev. D 92, 075027 (2015)
  doi:10.1103/PhysRevD.92.075027
  [arXiv:1407.0797 [hep-ph]].
J. M. Hoff da Silva and S. H. Pereira,
  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]].
S. Kouwn, J. Lee, T. H. Lee and P. Oh,
  ``Dark spinor model with torsion and cosmology,''
  Mod. Phys.  Lett. A  28, 1350121 (2013)
  doi:10.1142/S0217732313501216
  [arXiv:1211.2981 [gr-qc]].
J. Lee, T. H. Lee, P. Oh, T. H. Lee and P. Oh,
  Conformally-coupled dark spinor and FRW universe,
  Phys. Rev. D 86, 107301 (2012)
  doi:10.1103/PhysRevD.86.107301
  [arXiv:1206.2263 [gr-qc]].
C. G. Boehmer, J. Burnett, D. F. Mota and D. J. Shaw,
  Dark spinor models in gravitation and cosmology,
  JHEP 1007, 053 (2010)
  doi:10.1007/JHEP07(2010)053
  [arXiv:1003.3858 [hep-th]].
H. Wei,
  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]].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]].
D. Gredat and S. Shankaranarayanan,
  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]].
S. H. Pereira and T. M. Guimarães,
  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 .
C. G. Boehmer and D. F. Mota,
  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]].
M. Chaves and D. Singleton,
  A Unified Model of Phantom Energy and Dark Matter,
  SIGMA 4, 009 (2008)
  doi:10.3842/SIGMA.2008.009
  [arXiv:0801.4728 [hep-th]].
C. G. Boehmer,
  Dark spinor inflation: Theory primer and dynamics,
  Phys. Rev. D 77, 123535 (2008)
  doi:10.1103/PhysRevD.77.123535
  [arXiv:0804.0616 [astro-ph]].

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]].
D. V. Ahluwalia,
  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].
D. V. Ahluwalia,
  Evidence for Majorana neutrinos: Dawn of a new era in space-time structure,
  hep-ph/0212222 https://arxiv.org/abs/hep-ph/0212222 .
D. V. Ahluwalia,
  Extended set of Majorana spinors, a new dispersion relation, and a preferred frame,
  hep-ph/0305336 https://arxiv.org/abs/hep-ph/0305336 .
V. V. Dvoeglazov,
  Neutral particles in light of the Majorana-Ahluwalia ideas,
  Int. J. Theor. Phys.  34, 2467 (1995)
  doi:10.1007/BF00670779
  [hep-th/9504158].
中。

阿鲁瓦利亚在2017年解释了如何规避温伯格不走定理。同样在2017年发现D. V. Ahluwalia,
Evading Weinberg's no-go theorem to construct mass dimension one fermions: Constructing darkness 
Europhysics Letters 118 (2017) no.6, 60001 
DOI: 10.1209/0295-5075/118/60001. R. J. Bueno Rogerio, J. M. Hoff da Silva, M. Dias, S. H. Pereira, Effective lagrangian for a mass dimension one fermionic field in curved spacetime, [arXiv:1709.08707 [hep-th]], https://arxiv.org/abs/1709.08707 ，质量维度一费米子即使没有宇宙学常数，也能通过量子效应诱导一个“宇宙学常数”项。这些导致非消失的效应可能是早期宇宙阶段膨胀阶段的原因。此外，对于较晚的演化，对应于具有时变宇宙学项的模型，这种量子效应与先前的最新研究一致S.H. Pereira et al.
Λ(t) cosmology induced by a slowly varying Elko field, JCAP 1701, no. 01, 055 (2017)
  doi:10.1088/1475-7516/2017/01/055
  [arXiv:1608.02777 [gr-qc]].。

参考文献

Category:暗物质
Category:量子场论
Category:旋量