Generalized and Modified Quantum Field Theories

In General > s.a. canonical quantum gravity; fock space; poincaré group; quantum fields in curved spacetime; types of quantum field theories.
* Motivation, limits of validity: A natural UV cutoff in the validity of quantum field theory is expected from quantum gravity or string theory, and would help solve divergence problems.
* Galilei-invariant: The quantum version of a field theory which is not relativistically invariant, but only invariant under the Galilei transformations; In it, there is no particle creation and annihilation.
* Higher-derivative theories: They are often assumed to have ghosts, but in reality it is the (fourth + second)-order theory with a mass parameter m that has ghosts, while the pure fourth-order one is a singular limit and doesn't; This arises in the linearization of conformal gravity.
* Non-local: Several, differently motivated attempts at non-local (not generated by pointlike fields) relativistic particle theories have been made, the most recent one being quantum field theory on non-commutative spacetime.
@ Limits to quantum field theory: Cohen et al PRL(99)ht/98 [entropy bounds and large V's]; Carmona & Cortés PRD(02)ht/00 [100 TeV cutoff, and quantum gravity]; > s.a. quantum-gravity phenomenology.
@ Quaternionic: Adler CMP(86); Brumby & Joshi FP(96)ht [consequences].
@ Non-Fock Hilbert spaces: Tsirelson ht/99 [fermions].
@ Finite-temperature: Ccapa Ttira et al PRD(08)-a0803 [dual path-integral representations]; > s.a. stochastic quantization.
@ Higher-derivative theories: Weldon AP(03); Nguyen a0709 [self-interacting scalar field]; > s.a. Pais-Uhlenbeck Model.
@ Non-local: Cornish IJMPA(92); Breckenridge et al CQG(95)ht [in quantised spacetime]; Barci et al IJMPA(96)ht/95; Amorim & Barcelos-Neto JMP(99) [non-local massive s = 1]; Piacitelli JHEP(04) [diagram rules]; Schroer AP(05)ht/04 [rev]; Wang JMP(08); > s.a. causality, quantum systems, types of field theories.
@ Over a Galois field: Lev ht/02 [and spin-statistics], ht/02 [supersymmetry], ht/04 [general].
@ Other types: Anco & Wald PRD(89) [algebra-valued fields]; Haag CMP(93) [characterizing models]; Ribaric & Sustersic ht/97 [transport-theoretic], FizB(02)ht/01 [finite alternative theory]; Yang ht/98-in, ht/98 [as effective theory from finite one]; Dürr et al JPA(05)qp/04 [Bell-type Markov processes/trajectories]; Balakov et al CMP(07) [bilocal, scalar]; > s.a. perfect fluids.

Deformed and Quantum-Gravity Motivated Theories > s.a. non-commutative field theory [including braided].
@ General references: Gadiyar ht/96; Hurth & Skenderis NPB(99)ht/98, LNP(00)ht/98 [with symmetries]; García-Compeán et al IJMPA(01)ht/99 [scalar and abelian gauge theory], JPA(02)ht/01 [second quantization of Schrödinger equation]; Kosinski et al ht/00-in, ht/00-in; Iorio et al AP(01)ht [deformation and curved spacetime]; Bezerra et al PRD(02), PRD(02) [q-deformed, perturbative]; Dito m.QA/02-in [covariant field theory]; Sardanashvily ht/02 [polysymplectic]; Hirshfeld & Henselder AP(02)ht [star products]; Matsuo & Shibusa MPLA(06)ht/05 [based on gup]; Induráin & Liberati PRD(09)-a0905 [with non-canonical commutation relations, and DSR].
@ Generalized background: Kaiser AP(87) [complex spacetime]; Eyink CMP(89), CMP(89) [fractal spacetime]; Birmingham & Rakowski MPLA(94) [simplicial complex, intersection form action]; White et al a0812 [signature-changing]; Weinfurtner et al a0905-in [in analog gravity].
@ With fundamental length scale: Brüning & Nagamachi JMP(04) [in terms of ultra-hyperfunctions]; Hossenfelder CQG(08)-a0712.
@ Discrete: Kur'yan in(91) [discrete spacetime]; Norton & Jaroszkiewicz JPA(98) [discrete time]; Häußling AP(02) [and non-commutative geometry]; > s.a. quantum field theory on graphs.
> Related topics: see analysis [fractional derivatives]; non-standard analysis; quantum field theory states [including non-equilibrium].

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