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].
@ 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 a1609 [algebraic form].
@ 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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