Spin and Spinors| 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];
Cahill EJP(21)-a2104 [and spin-1/2 fields, pedagogical].
@ 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; formulations of general
relativity; 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 (for 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;
in D'Ariano a1110-conf [simulation with a quantum computer];
Durfee & Archibald a1201;
Aerts & Sassoli de Bianchi SC(17)-a1501 [and directions in Euclidean space];
Ertem a1801-ln [geometry and applications].
@ In quantum mechanics: Budinich NCB(08)-a0803;
Ovsiyuk et al HNGP-a1410-conf [quantum effects];
Samuel a1907 [twisted spin];
> s.a. relativistic quantum mechanics [relativistic spin operator].
@ 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];
Giacomini et al a1811 [operational definition, quantum reference frames];
> s.a. electronic technology [spin currents, spintronics].
> And particles:
see electron; fermions;
hadrons; neutron;
proton; spinning
particles; spinors in field theory; 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];
Heiner et al a1811 [non-linear dynamics and chaos];
> 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].
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