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].
@ Classification: Miralles & Pozo JMP(06) [unified description of different types]; da Silva & da Rocha PLB(13)-a1212 [Lounesto algebraic classification]; Bonora et al JHEP(15)-a1411 [in arbitrary dimensions and signatures].
@ 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 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 [alternative approach]; > 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 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 a1604 [algebraic spinors, vacuum, creation and annihilation operators].
@ Other phenomenology: Vager & Vager PLA(12) [spin order without magnetism]; > s.a. coupled spin models; magnetism.
> Other topics: see Covariance; deformation quantization; inertia; lie derivatives; Pin Group.


main pageabbreviationsjournalscommentsother sitesacknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 15 jul 2017