Spin and Spinors  

In General
* Idea: Spinors are elements of vector spaces carrying spinor representations of the rotation group, where a 2π 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, \(\mathbb C\)) spinor and its complex conjugate); They can however have geometrical interpretations as generalized geometrical objects.
> Discrete / generalized settings: see causal sets; finsler spaces; lattice field theories; non-commutative theories.

General References > s.a. clebsch-gordan theory.
@ Books and intros: Chevalley 54; Cartan 66; in Wald 84; Penrose & Rindler 84, 86; Benn & Tucker 87; Lawson 89; Esposito 95; Hladik 99; Carmeli & Malin 00; Cahill & Cahill EJP(06)ht/05 [Majorana & Dirac, pedagogical]; Lachièze-Rey a1007-conf; Torres del Castillo 10; Todorov BulgJP(11)-a1106 [intro]; Steane a1312 [intro]; Rios & Straume a1402-book [correspondence between quantum and classical mechanics].
@ History and reviews: van der Waerden (tr Pasa) NGWG(29)-a1703 [spinor analysis]; Fröhlich a0801-ln; Milner a1311-conf, IJMPcs-a1502.
@ Other general references: Pauli ZP(25); Bergmann PR(56); Milnor EM(63); Plebański pr(64); Pirani in(65); Penrose in(68); Clarke GRG(71); Lee GRG(73); Hitchin AiM(74); Plebański pr(74); Isham PRS(78); Whiston JPA(78); meeting 6.06.1984; Magnon JMP(87); Liu JMP(91); Sharma AP(91); Sverdlov a0808 [novel definition]; Andreev PhD-a1204 [in 6D Riemannian spaces]; Cederwall JHEP(12) [complex geometry of D = 10 pure spinor space]; Budinich JPA(14)-a1208 [null vectors and spinors in Clifford algebra].

Spin in Physical Theories > s.a. coupled-spin models; spinors in field theory; types of spinors [including ELKO, and representations].
* Idea: Spinors are used in physics mainly for defining fermions; They are natural in quantum mechanics, but they are also very useful in classical theories (fr example, Witten's proof of the positive-energy theorem, the spinorial decomposition of the curvature tensor, principal null directions of Weyl tensors).
@ Nature and use: Rindler AJP(66)oct; Ohanian AJP(86)jun; Morrison SHPMP(07) [ontological and epistemic status]; Kosmachev a0709; Budinich NCB(08)-a0803 [and quantum mechanics]; in D'Ariano a1110-conf [simulation with a quantum computer]; Durfee & Archibald a1201; Ovsiyuk et al HNGP-a1410-conf [quantum effects]; Aerts & Sassoli de Bianchi a1501 [and directions in Euclidean space].
@ Phenomenology / experiments: Christian IJTP(15)-a1211 [macroscopic observability of sign change under 2π rotations]; Lin et al PRL(15) [measuring the spin of individual atoms]; > s.a. electronic technology [spin currents, spintronics].
> And particles: see electron; Fermions; hadrons; neutron; proton; spinning particles; types of particles.

Models, Geometrical Interpretations and Related Topics
@ Spinorial chessboard: Budinich & Trautman JGP(87), 88.
@ Models, geometric interpretations: Ogievetsky & Polubarinov JETP(65); Newman & Winicour JMP(74) [from worldline in complex Minkowski space, and twistors]; Ulmer IJTP(77); Bugajska IJTP(79); 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 a0803; Creutz AP(14) [emergent spin from spinless particle on a lattice]; McLachlan et al JNS(16)-a1505 [Hamiltonian, time-discretization scheme]; Novak & Runkel a1506 [from networks of topological defects]; > s.a. Kinks.
@ Related topics: Sachs BJPS(89); Weigert JOB(04)qp/99 [spin coherent states]; Ferrara FdP(01)ht/00-proc [and spacetime superalgebras]; Kobayashi ht/05 [origin of spin?]; García-Parrado & Martín-García CPC(12)-a1110 [Mathematica package]; Céleri et al PRA(16)-a1607 [spin, localization and uncertainty].


main pageabbreviationsjournalscommentsother sitesacknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 30 mar 2017