Spin and Spinors

In General > s.a. spin models; spinors in field theory.
* Idea: Spinors are elements of vector spaces carrying spinor representations of the rotation group, where a 2 rotation is –1.
* Interpretation: Spinors themselves cannot have a physical interpretation, but bilinear products of spinors and complex conjugate spinors can (e.g., a 4D null vector can be seen as a tensor product of an SL(2,C) spinor and its complex conjugate); They can however have geometrical interpretations as generalized geometrical objects.
* Kähler spinors: Polynomials of differential forms.
* Applications: Spinors are natural in quantum mechanics, but they are also very useful in classical theories; Witten's proof of the positive energy theorem, spinorial decomposition of the curvature tensor, principal null directions of Weyl tensors.

Types and Related Topics > s.a. 2-spinors; 4-spinors; Pin Group; spin structure.
* ELKO spinors: "Eigenspinoren des Ladungskonjugationsoperators", or dual-helicity eigenspinors of the charge conjugation operator.
@ General references: 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]; Miralles & Pozo JMP(06) [unified description of different types]; Poplawski a0710 [covariant derivatives].
@ Kähler spinors: Becher & Joos ZPC(82) [lattice]; Bullinaria AP(86); Jourjine PRD(87) [quantization]; Shimono PTP(90) [and lattice gravity]; Borstnik & Nielsen ht/99-in, PRD(00)ht/99, ht/00; Jourjine a0805.
@ ELKO spinors: 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 [and Dirac spinors].
> Other topics: see deformation quantization; inertia.

References > s.a. clebsch-gordan; finsler spaces; lattice field theories; non-commutative theories.
@ Books and intros: Chevalley 54; E Cartan 66; in Wald 84; Penrose & Rindler 84, 86; Benn & Tucker 87; Lawson 89; Esposito 95; Carmeli & Malin 00; Cahill & Cahill EJP(06)ht/05 [Majorana & Dirac, pedagogical].
@ Nature and use: Rindler AJP(66); Ohanian AJP(86); Morrison SHPMP(07) [ontological and epistemic status]; Kosmachev a0709; Budinich a0803 [and quantum mechanics].
@ Other general references: Bergmann PR(56); Milnor EM(63); Plebanski pr(64); Pirani in(65); Penrose in(68); Clarke GRG(71); Lee GRG(73); Hitchin AiM(74); Plebanski pr(74); Isham PRS(78); Whiston JPA(78); meeting 6.06.1984; Magnon JMP(87); Liu JMP(91); Sharma AP(91); Fröhlich a0801-ln [history and rev].
@ Generalized: Avis & Isham CMP(80); Trautman & Trautman JGP(94); Toppan ht/05-in [quaternionic, octonionic].
@ Spinorial chessboard: Budinich & Trautman JGP(87), 88.
@ Classical models: Newman & Winicour JMP(74) [from worldline in complex Minkowski space, and twistors]; Barut & Meystre PLA(82) [classical vs quantum spins]; Czachor FPL(92)qp/02 [and Bell's theorem]; Hadley CQG(00)gq [geons in pure gravity]; Bosanac FdP(01)qp; Mauro PLB(04)qp [from geometric de-quantization]; Sverdlov a0802 [geometrical description]; Savasta & Di Stefano 0803; > s.a. Kinks.
@ Related topics: Sommers JMP(80) [spatial]; Yip JMP(83) [2D]; Sachs BJPS(89); Weigert JOB(04)qp/99 [spin coherent states]; Dray & Manogue ht/99-in [quaternionic]; Ferrara FdP(01)ht/00-in [and spacetime superalgebras]; Carrion et al JHEP(03)ht [quaternionic, octonionic]; Kobayashi ht/05 [origin of spin?].

Spinor Irreducible Representations
* Pattern: (repeats itself mod 4)

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