Types of Spinors| Types of Spinors |
In General, Main Types > s.a. 2-spinors;
4-spinors [Majorana and Dirac spinors]; spin structure.
@ General references: Sommers JMP(80) [spatial];
Yip JMP(83) [2D];
Trautman ln(87) [Dirac and Chevalley];
Goncharov IJMPA(94) [real];
van Nieuwenhuizen & Waldron PLB(96) [Euclidean];
Hamilton JMP(97) [hypercomplex numbers];
Faber FBS(01)ht/99 [topological fermions];
Friedman & Russo FP(01) [geometry, Jordan triples and spin factors];
Rodrigues JMP(04)mp/02 [Dirac-Hestenes spinors];
Pal AJP(11)may-a1006 [Dirac, Majorana, and Weyl fermion fields, pedagogical];
Budinich AACA(15)-a1405 [spinors of zero nullity];
Fredsted a1811
[coupled to gravity, using only world indices].
@ Lounesto algebraic classification:
da Silva & da Rocha PLB(13)-a1212;
Arcodía et al EPJC(19)-a1902 [and Heisenberg spinors];
Coronado et al a1909;
Bueno EPJC(19)-a1911.
@ Other classification: Miralles & Pozo JMP(06) [unified description of different types];
Bonora et al JHEP(15)-a1411 [in arbitrary dimensions and signatures];
Bonora et al EPJC(18)-a1711 [and second quantization];
Coronado et al a1906 [beyond Lounesto].
@ Irreducible representations: Varlamov a1412 [modulo-8 periodicity];
Curtright et al PLA(16)-a1607 [multiplicities in Kronecker products];
Polychronakos & Sfetsos NPB(16)-a1609 [decomposition of arbitrary products into irreducible SU(2) representations];
Hoff da Silva et al EPJC(17)-a1702.
@ Covariant derivative: Popławski a0710;
Shapiro a1611.
@ Hamiltonian dynamics: Kaur et al PLA(14) [mechanical analogues];
McLachlan et al MoC(16)-a1402 [discrete time];
> s.a. dirac fields; coupled spin models.
@ Semiclassical description:
Bulgac & Kusnezov AP(99);
Deriglazov AP(12)-a1107,
Deriglazov & Pupasov-Maksimov Sigma(14)-a1311 [without Grassmann variables].
> And physical theories:
see dirac fields; coupled-spin
models; magnetism; quantum
particles [relativistic]; spinors in field theory.
ELKO Spinors
* Idea: "Eigenspinoren des
Ladungskonjugationsoperators", or dual-helicity eigenspinors of the charge
conjugation operator; Spin-1/2 fermions with mass dimension 1 proposed in
2005 by Ahluwalia and Grumiller, and suggested as a dark matter candidate.
@ General references:
da Rocha & Rodrigues MPLA(06)mp/05 [and Lounesto classification];
Böhmer AdP(06)gq [and Einstein-Cartan theory],
AdP(07)gq [in curved spacetime, coupled Einstein-ELKO fields];
da Rocha & Hoff da Silva JMP(07)-a0711,
IJMPA(09)-a0903 [and Dirac spinors],
IJGMP(09)-a0901 [and gravity];
Fabbri MPLA(10)-a0911,
MPLA(10)-a0911 [causal propagation];
Lee a1011 [in 1+1 dimensions];
Fabbri PLB(11)-a1101 [most general dynamical theory];
Lee PhD(12)-a1306 [symmetries];
Hoff da Silva & Pereira JCAP(14)-a1401 [in spatially flat FLRW spacetimes];
Fabbri & Vignolo IJMPD(14)-a1407 [and torsion];
Ahluwalia & Nayak IJMPD(14)-a1502 [causality and Fermi statistics];
Bueno et al a1706-wd [alternative approach];
Ahluwalia & Sarmah EPL(19)-a1810 [spatial rotations];
Nieto MPLA(19)-a1907 [generalized Elko theory];
Ahluwalia EPJST-a2103 [rev];
> s.a. Conformal Gravity;
Wikipedia page.
@ As dark matter:
Ahluwalia et al PLB(10);
Dias et al PLB(12)-a1012 [and the LHC];
Gillard a1109,
RPMP(12).
@ Other cosmology: Wei PLB(11)-a1002 [as dark-energy candidate];
Basak et al JCAP(13)-a1212 [inflationary attractor behavior];
de Oliveira & Rodrigues PRD(12)-a1210 [preferred axis];
Kouwn et al MPLA(13) [with torsion];
Pereira et al JCAP(14)-a1402 [attractor behavior];
Pereira & Guimarães JCAP(17)-a1702.
@ Other phenomenology: Boehmer & Burnett a1001-MG12 [dark spinors].
Other Types and Related Topics
> s.a. poincaré group [representations, including continuous spin].
* Kähler spinors:
Polynomials of differential forms.
@ Kähler spinors:
Becher & Joos ZPC(82) [lattice];
Bullinaria AP(86);
Jourjine PRD(87) [quantization];
Shimono PTP(90) [and lattice gravity];
Mankoč Borštnik & Nielsen ht/99-conf,
PRD(00)ht/99,
ht/00;
Jourjine a0805-wd;
Kruglov EPJC(10)-a0911
[massless, Belinfante energy-momentum tensors and canonical quantization];
Jourjine PLB(10)-a1005 [and chiral fermion mass terms].
@ Quaternionic:
Dray & Manogue ht/99-proc;
Carrion et al JHEP(03)ht,
Toppan AIP(05)ht [and octonionic];
Fredsted JMP(09)-a0811 [in curved spacetime].
@ Other, and generalized spinors:
Ogievetsky & Polubarinov JETP(65);
Avis & Isham CMP(80)
[with internal symmetry group G/\(\mathbb Z\)2];
Trautman & Trautman JGP(94);
Batista JGP(14)-a1310 [pure subspaces];
Vassilevich JMP(15)-a1508 [symplectic spinors, spectral geometry];
Pitts a1509-proc [and Ockham's razor];
Monakhov PPN(17)-a1604 [algebraic spinors, vacuum, creation and annihilation operators];
Coronado et al EPJC(19)-a1812 [type-4 spinors].
@ Other phenomenology: Vager & Vager PLA(12) [spin order without magnetism];
Beghetto et al AACA(18)-a1810 [and black-hole physics];
> s.a. coupled-spin models; magnetism.
> Other topics:
see Covariance; deformation quantization;
inertia; lie derivatives;
Pin Group.
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