Generalized Dirac Fields| Generalized Dirac Fields |
In General
> s.a. types of field theories ["shifted differential equations"].
@ As a quantum random walk:
Bracken et al qp/06;
Arrighi et al JPA(14)-a1307 [in all dimensions];
> s.a. random walk.
@ Other formulations: Evans FP(90);
Augenstein PT(95)may;
Robson & Staudte JPA(96),
Staudte JPA(96);
Dolby & Gull AP(01)ht;
Efthimiades qp/06 [from averaged energy relation];
Mulligan AP(06) [decoupling into 2-spinor equations];
Aastrup et al a1003 [from abstract spectral triple];
Akhmeteli JMP(11)-a1008,
EPJC(13)-a1111-conf,
a1502 [in terms of one real function];
Trzetrzelewski a1101 [with generalized mass term];
Earle a1102 [master equation approach].
@ Square root: Szwed APPB(06)ht/04,
Bzdak & Szwed EPL(05)ht/04 [and supersymmetric field theory];
> s.a. modified electromagnetism.
@ Non-linear: Czachor PLA(97) [Nambu-type];
Ng & Parwani Sigma(09)-a0707,
MPLA(10)-a0805 [and neutrino oscillations];
Xu et al JCP(13) [numerical];
Marchuk a1307.
@ Non-local: Galiautdinov & Finkelstein JMP(02)ht/01 [chronon corrections];
Mashhoon PRA(07)ht/06 [accelerated frames].
@ Geometric approaches: Olkhov JPCS(07)-a0706;
Sochichiu JPA(13)-a1112 [emergence in a dynamical lattice model];
Fefferman & Weinstein CMP(14)-a1212 [emergence for wave packets in 2D honeycomb lattice potentials];
Fabbri IJTP(14) [8D representation];
> s.a. particles [models].
@ Other dimensionalities:
Kocinski JPA(99) [5D form];
Sánchez-Monroy & Quimbay AP(14)-a1403 [in 1+1 and 2+1 dimensions].
@ Fractional: Raspini PS(01) [of order 2/3];
Muslih et al JPA(10).
@ Related topics: Dirac PRS(71),
PRS(72) [positive-energy];
Uzes & Barut FP(98) [as excitations of scalar fields];
Loide et al JPA(01);
Chang qp/01 [spacelike/tachyonic];
Baylis JPA(02)qp;
Camacho & Macías PLB(04)ht [proposed tests];
Kim JGP(06);
Novello EPL(07)-a0705 [Dirac linear fermions in terms of non-linear Heisenberg spinors];
Wu et al IJTP(12) [at finite temperature];
Sharma & Singh IJModP(14)-a1405 [as the torsion-dominated, gravity-free limit of a geometric framework];
Heaney a1410/FP [interpretation without Zitterbewegung];
> s.a. Bieberbach Manifold.
Discrete, Quantum-Gravity Motivated
> s.a. doubly special relativity; finsler geometry;
non-commutative field theory; quantum group.
@ Discrete: Selesnick JMP(94) [quantum net];
Kauffman & Noyes PLA(96)ht [1+1 dimensions];
Burda et al PRD(99) [on a random lattice];
Das CJP(10)-a0811 [covariant discrete phase space];
Roiesnel PRD(13)-a1211 [covariant lattice Dirac operator];
Sushch RPMP(14)-a1307 [discrete analog of the Dirac-Kähler equation];
Sushch DDEA(16)-a1509 [discrete analog in the Hestenes form];
Sushch PSM-a1609 [algebraic form];
Borrelli et al a1912 [non-linear, on a graph].
@ Lorentz-violating:
Lehnert JMP(04) [in Lorentz-violating standard model];
Ferreira & Moucherek IJMPA(06) [and CPT-violating];
Colladay et al JPA(10) [dispersion relation, factorized];
Kruglov PLB(12) [and particles in an external magnetic field].
@ Deformed, with minimal length: Nozari & Karami MPLA(05)ht;
Chargui et al PLA(10) [2D];
Shokrollahi RPMP(12)-a1208;
Antonacci Oakes et al EPJC(13)-a1308 [hydrogen atom ground state];
> s.a. minkowski space [κ-deformed].
@ Related formulations: Célérier & Nottale
ht/01/PRD,
EP(03)ht/02 [in scale relativity];
Kull PLA(02)qp [on a rational subset of 2D Minkowski space].
Different Mathematical Frameworks
@ And Clifford algebra:
Beil IJTP(04) [Clifford numbers and Peirce logic];
Baugh et al IJTP-qp/04-conf [Clifford-algebra logic];
da Rocha & Rodrigues AACA(08)mp/05-conf [diffeomorphism and local Lorentz invariance].
@ Quaternionic: Lanczos ZP(29)phy/05,
ZP(29)phy/05,
ZP(29)phy/05;
Dray & Manogue ht/99-proc [& octonionic];
De Leo FPL(01)ht; > s.a. quaternions.
@ Octonionic: Gogberashvili IJMPA(06)ht/05;
De Leo & Abdel-Khalek PTP(96)ht;
> s.a. Octonions.
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