Dirac Equation / Fields  

Dirac Equation > s.a. dirac fields in curved spacetime [eigenvalues]; lagrangian systems; quantum dirac fields.
$ Def: The equation for a 4-component spinor , describing spin-1/2 particles, given by

(i aa – m) = 0 ,   a = Dirac matrices .

* In 2D: With potentials v and w, ( p + v + 5w) = E , with , , 5 Pauli matrices, p momentum.
* Probability density: j 0:= , positive-definite.
* Applications: Yields the Sommerfeld fine structure for the H atom energy levels.
* Properties: Has negative-energy states, interpreted as positrons when quantized.

References > s.a. huygens principle; lattice field theory.
@ General: Dirac PRS(36); in Bethe & Jackiw 68; Laporte & Uhlenbeck PR(31); Ng & van Dam PLA(03)ht/02 [derivation, lattice]; Wilczek IJMPA(04); Gsponer & Hurni phy/05-in [history].
@ Evolution: Adler & Jacob JMP(96) [initial-value formulation]; Bigazzi & Lusanna IJMPA(99) [Hamiltonian, observables]; Lukyanenko & Lukyanenko gq/06 [path integral representation].
@ Numerical: Mocken & Keitel JCP(04).
@ Alternative formulations: Evans FP(90); Augenstein PT(95)may; Robson & Staudte JPA(96), Staudte JPA(96); Dolby & Gull AP(01)ht; Bracken et al qp/06 [as quantum random walk]; Efthimiades qp/06 [from averaged energy relation]; Mulligan AP(06) [decoupling into 2-spinor equations].
@ Related topics: Lanczos ZP(29)phy/05, ZP(29)phy/05, ZP(29)phy/05; Fauser ht/96-in [quantum field theory point of view]; Konopelchenko JPA(97) [and Gauss-Codazzi equations]; Solomon qp/99 [inconsistencies?]; Marchuk NCB(01)mp/00, mp/00 [as tensor equation]; Liu mp/01 [vector representation]; Ord qp/02-in [from classical statistical mechanics]; Solomon qp/02, qp/03 [and gauge invariance], ht/03 [Schwinger term issues]; Mosna & Vaz PLA(03) [tomographic reconstruction]; Chavoya-Aceves NCB(03) [de Broglie-Bohm type model]; Arminjon FPL(06) [from classical Hamiltonian].

Systems and Solutions > s.a. aharonov-bohm; dirac fields in curved spacetime; Dirac Matrices; particle models; solitons.
@ General references: Benguria et al JPA(00) [ potential]; de Castro & Franklin IJMPA(00)hp, hp/00-in; Hiller AJP(02)qp/01 [1+1 scalar potential]; Thaller qp/04 [wave packet visualization]; Voronov et al TMP(07)qp/06 [strong Coulomb field]; Giachetti & Sorace a0706 [confining potentials].
@ V(r): Goodman & Ignjatovic AJP(97) + comments; Esposito & Santorelli JPA(99)ht; Bose et al PLA(01); Alhaidari PRL(01)ht, IJMPA(03); Dong PS(03) [2+1 Coulomb]; de Castro AP(04) [2D, linear + Coulomb-like V]; Ciftci et al PRA(05)mp [D dimensions].
@ Cylindrically symmetric: Booth & Radford JMP(97)ht/96; Skarzhinsky & Audretsch JPA(97)ht [in B field].
@ Scattering: Dombey & Kennedy JPA(02)ht/01; Murguia & Moreno JPA(03)qp/02 [in B]; Kennedy et al IJMPA(04)mp [phase shifts].
@ Potential barrier: Dombey et al PRL(00)ht [transmission]; De Leo & Rotelli EPJC(06)ht [multiple scattering], ht/06 [and Klein-like paradox].
@ Couplings: Rivas JPA(07)ht [two coupled particles].
@ Related topics: Gulveren et al PS(01) [in Yukawa field]; Chrusciel & Bartnik m.DG/03 [boundary value problem]; Dürr & Pickl JMP(03) [flux across surfaces theorem]; D'Ancona & Fanelli m.AP/05 [with em potential, dispersion]; Bourouaine EPJC(05)mp [in plane electromagnetic wave]; Tenjinbayashi et al AP(07) [on a torus, zero-modes]; Bhattacharya a0705 [uniform magnetic field].
> Related phenomena: see Dirac Sea; electromagnetism; Induced Gravity; Klein Paradox; quantum effects [tunneling].

Generalizations, Modifications > s.a. Bieberbach Manifold; finsler geometry; non-commutative fielod theory; quantum group.
@ Quaternionic: Lanczos &(29); Dray & Manogue ht/99-in [& octonionic]; De Leo FPL(01)ht; > s.a. Quaternions.
@ Octonionic: Gogberashvili IJMPA(06)ht/05; De Leo & Abdel-Khalek PTP(96)ht.
@ Square root: Szwed APPB(06)ht/04, Bzdak & Szwed EPL(05)ht/04 [and susy field theory]; > s.a. modified electromagnetism.
@ Discrete: Selesnick JMP(94) [quantum net]; Kauffman & Noyes PLA(96)ht [1+1]; Burda et al PRD(99) [random lattice].
@ Non-linear: Czachor PLA(97) [Nambu-type]; Ng & Parwani a0707, a0805 [and neutrino oscillations].
@ Non-local: Galiautdinov & Finkelstein JMP(02)ht/01 [chronon corrections]; Mashhoon PRA(07)ht/06 [accelerated frames].
@ Lorentz-violating: Lehnert JMP(04) [in Lorentz-violating standard model]; Ferreira & Moucherek IJMPA(06) [and CPT-violating].
@ And Clifford algebra: Beil IJTP(04) [Clifford numbers and Peirce logic]; Baugh et al qp/04/IJTP [Clifford algebra logic]; da Rocha & Rodrigues mp/05-in [diffeomorphism and local Lorentz invariance].
@ Geometric approaches: Olkhov a0706-in; > s.a. particles [models].
@ Other topics: Dirac PRS(71), PRS(72) [positive-energy]; Uzes & Barut FP(98) [as excitations of scalar fields]; Kocinski JPA(99) [5D form]; Loide et al JPA(01); Raspini PS(01) [fractional, of order 2/3]; Chang qp/01 [spacelike/tachyonic]; Célérier & Nottale ht/01/PRD, EP(03)ht/02 [in scale relativity]; Baylis qp/02/JPA; Kull PLA(02)qp [on rational subset of 2D Minkowski]; Camacho & Macías PLB(04)ht [proposed tests]; Nozari & Karami MPLA(05)ht [with minimal length]; Kim JGP(06); Novello a0705 [Dirac linear fermions ito non-linear Heisenberg spinors].

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Send feedback and suggestions to bombelli at olemiss.edu – Modified 13 jun 2008