Low-Spin Field Theories  

Spin-0 Fields > see scalar field theories.

Spin-1/2 Fields > s.a. boundaries in field theory; dirac field theory; spinors.
* Idea: Fermions, can be considered as a collection of 2-state oscillators; Descriptions include the Dirac equation and the Feshbach-Villars equation.
@ Classical: Gaioli & García Álvarez FP(98)ht; Deriglazov & Gitman MPLA(99)ht/98; Kochetov JPA(00) [in B]; Pestov ht/01.
@ Related topics: Chamblin ht/97-in [classification of fermions]; Mickelsson PLB(99)ht [with boundary]; McLenaghan et al PRS(00) [symmetries]; Guettou & Chetouani PS(06) [Feshbach-Villars equation and pair creation].

Spin-1 (Vector) Fields > s.a. electromagnetism; gauge theory; Kemmer Equation; types of dark energy.
* History: The correct massive wave equation was derived by Lanczos, and rediscovered by Proca in 1936.
@ General references: Mweene qp/99 [vectors and operators]; Zecca NCB(00) [on Schwarzschild], NCB(02) [with torsion].
@ Massive: Proca CRAS(36); Gazeau & Takook JMP(00) [quantum on de Sitter]; Arias & Pérez-Mosquera ht/04-in [Cremmer-Scherk & Proca]; Gsponer & Hurni phy/05-in [history]; Zecca NCB(05) [in expanding universe]; > s.a. electroweak theory [W bosons]; lagrangian systems.
> Quantum theories: see quantum field theory in curved spacetime; types of quantum field theories [non-local].

Spin-3/2 Fields > s.a. Gyromagnetic Ratio; Rarita-Schwinger; supergravity; twistors; types of gauge theories.
* History: A theory was first formulated by Pauli & Fierz; The standard one is the simplified one, based on the Rarita-Schwinger equation, which is plagued by problems; Belinfante calculated the gyromagnetic ratio g = 2/3.
@ General references: Gupta PR(54); Robinson GRG(95); Kudrya TMP(95) [exact sets]; Frauendiener et al CQG(96) [m = 0]; Torres del Castillo & Herrera IJTP(96) [in Minkowski]; Deser et al PRD(00)ht [Q, m 0]; Pascalutsa PLB(01)hp/00 [consistency]; Shima & Tsuda PLB(01) [Nambu-Goldstone fermion]; Gsponer & Hurni HJ(03)mp/02 [Lanczos quaternion approach]; Villanueva et al FP(03) [electromagnetic coupling]; Kruglov IJMPA(06)ht/04 [as sqrt of Proca equation]; Napsuciale et al EPJA(06)hp; Darkhosh a0712-wd [massive, consistency, coupled to electromagnetism in supergravity].
@ In curved spacetime, cosmology: Maroto & Mazumdar PRL(00)hp/99 [early universe]; Hayashi MPLA(01)ht [twistors, torsion]; Zecca IJTP(07) [in Schwarzschild spacetime]; Pahlavan & Bahari IJTP(09) [in de Sitter pace, quantization].

Spin-2 Fields > s.a. asymtotic flatness at scri; graviton; gravity; types of gauge theories.
* Remark: They can be geometrized by the non-linear dynamics of general relativity (or as the torsion of a Cartan geometry); Consistency constraints on a free massless symmetric, rank-2, tensor field in a background uniquely require it to be the linear deviation about Einstein gravity; On the other hand, non-linear generalizations of a spin-2 linear field theory can have different symmetry groups.
* Field equations: Described by a symmetric hab; In the massless case,

cc hab + ab h – 2 c(a hb) c – ab cc h + ab cd hcd = 0 .

* Pauli-Fierz theory: A theory of massive charged spin-2 fields, e.g., the graviton; Arises also as effective 4D theory in brane models.
* van Dam-Veltman discontinuity: A discontinuity in the Pauli-Fierz formulation; The deflection angle in the background of a spherically symmetric gravitational field converges to 3/4 of the value predicted by the massless theory (linearized general relativity) as m → 0.
@ General references: in Wentzel 49; Wald PRD(86) [and general covariance], CQG(87), in(88); Cutler & Wald CQG(87); Heiderich & Unruh PRD(88); Buchbinder et al PLB(99)ht [in string theory], NPB(00)ht/99 [coupled to gravity]; Friedrich CQG(03) [near infty].
@ Pauli-Fierz theory: Fierz & Pauli PRS(39); Groot Nibbelink & Peloso CQG(05)ht/04 [covariant]: Boulanger & Gualtieri CQG(01)ht/00 [PT non-invariant deformation]; Obukhov & Pereira PRD(03) [teleparallel origin]; Georgescu et al CMP(04) [massless, spectral theory]; Leclerc gq/06 [gauge and reduction]; Osipov & Rubakov CQG(08)-a0805 [superluminal graviton propagation]; Hasler & Herbst RVMP(08) [Hamiltonians]; González et al JHEP(08) [duality]; Loss et al LMP(09) [degeneracy of eigenvalues of Hamiltonian].
@ van Dam-Veltman discontinuity: Carrera & Giulini gq/01 [m > 0, with electromagnetism]; Sato ht/05 [formulation with smooth m = 0 limit].
@ In (A)dS spacetime: Deser & Waldron PLB(01), Polishchuk TMP(04) [massive, AdS]; Gabadadze et al a0809 [massive, dS]; Zinoviev MPLA(09) [massless, electromagnetic interactions]; Zinoviev NPB(09)-a0901 [massive, electromagnetic interactions].
@ In other curved spacetime: Bengtsson JMP(95)gq/94; Novello & Neves CQG(02)gq [Fierz representation]; Deser & Henneaux CQG(07)gq/06 [re consistency]; Papini PRD(07)gq; Zecca IJTP(09) [in FRW spacetime].
@ Other massive spin-2 fields: Nair et al a0811 [from torsion, in curved spacetime].
@ In electromagnetic background: Klishevich & Zinoviev PAN(98)ht/97 [massive]; Novello et al ht/03 & ht/03, Deser & Waldron ht/03 [acausality].
@ Related topics: Boulanger et al ht/00-in [consistency]; Novello gq/02 [and torsion]; Magnano & Sokolowski AP(03) [and higher-derivative]; López-Pinto gq/04 [non-standard]; Zinoviev JHEP(05)ht [massive, dual formulation], NPB(07) [massive, possible interactions]; Blas JPA(07)ht-in [without ghosts or tachyons].

Other Types of Fields > see high-spin field theories; types of field theories.

main page – abbreviations – journals – comments – other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 22 aug 2009