Quantum Field Theory – Generalized and Modified Theories  

In General > s.a. fock space; poincaré group; quantum fields in curved spacetime; types of fields and types of theories [including non-Lagrangian].
* 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 theories: 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.
@ Generalized theories: Clarke IJTP(79), JPA(90) [group bundle theories]; Calcagni & Nardelli IJMPA(14)-a1306 [with spacetime-dependent couplings]; Kuwahara et al PLA(13)-a1307 [non-conservative]; Friedan a1605 [quantum field theories of (n−1)-dimensional extended objects].
@ Limits to quantum field theory: Cohen et al PRL(99)ht/98 [entropy bounds and large Vs]; 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].
@ Higher-derivative theories: Weldon AP(03); Nguyen a0709 [self-interacting scalar field]; Ghosh & Shankaranarayanan PRD(12)-a1211 [entanglement signatures of phase transition]; Talaganis a1707 [infinite-derivative scalar field action, unitarity]; Asorey et al a1802 [unitarity properties]; Buoninfante et al a1805 [infinite-derivative, ghost-free]; > s.a. Lee-Wick Models; Pais-Uhlenbeck Model.
@ Non-local theories: Yukawa PR(50) [s = 0, 1/2 or 1]; 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); Addazi & Esposito IJMPA(15)-a1502 [without acausality and non-unitarity]; Tomboulis PRD(15)-a1507 [UV finiteness, unitarity of amplitudes]; Belenchia et al PRD(16)-a1605 [low-energy signatures, proposed experiment, and quantum gravity]; Bernard et al a1903-Part; > s.a. causality; quantum systems; non-local field theories; unruh effect.
@ 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]; Ribarič & Šušteršič ht/97 [transport-theoretic], FizB(02)ht/01 [finite alternative theory]; Yang ht/98-conf, 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]; Finkelstein a1403, a1403 [quantum set algebra]; > s.a. Adelic Structures; homology [chain-complex-valued]; modified quantum mechanics [PT symmetry]; p-Adic Structures; perfect fluids.

Finite-Temperature / Thermal Field Theory > s.a. quantum statistical mechanics [thermofield dynamics]; stochastic quantization.
* Approaches: The main ones are the imaginary-time (Matsubara) formalism, the closed-time formalism and thermofield dynamics.
@ Introductions and reviews: Altherr IJMPA(93); Le Bellac 96; Das 97; Landshoff hp/97-ln; Andersen & Strickland AP(05) [perturbative]; Laine & Vuorinen 16.
@ General references: Ccapa Ttira et al PRD(08)-a0803 [dual path-integral representations]; Khanna et al 09; Fister & Pawlowski a1112 [Yang-Mills correlation functions]; Bischer et al a1901 [at high T].
@ Finite-temperature classical field theory: Gozzi & Penco AP(11)-a1008 [three approaches].
@ Related topics: Quirós HPA(94) [phase transitions]; Boyanovsky et al PRD(04)hp/03 [2D φ4 thermalization]; Kapusta & Gale 06; Meyer JHEP(09) [finite-volume effects]; Millington & Pilaftsis PRD(13)-a1211, JPCS(13)-a1302 [non-equilibrium, perturbative formulation].
> Systems and related topics: see de sitter spacetime; standard model; types of quantum field theories [finite-temperature effects].
> Online resources: see Wikipedia page.

Deformed and Quantum-Gravity Motivated Theories > s.a. canonical quantum gravity; 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]; Kosiński et al ht/00-proc, PAN(01)ht/00-proc; Bezerra et al PRD(02), PRD(02) [q-deformed, perturbative]; Dito m.QA/02-proc [covariant field theory]; Sardanashvily ht/02 [polysymplectic]; Hirshfeld & Henselder AP(02)ht [star products]; Matsuo & Shibusa MPLA(06)ht/05 [based on gup]; Carmona et al PRD(09)-a0905 [with modified commutation relations]; Induráin & Liberati PRD(09)-a0905 [with non-canonical commutation relations, and DSR]; Lechner et al LMP(13)-a1209 [equivalence of two deformation schemes].
@ On curved spacetimes: Iorio et al AP(01)ht [deformation and curved spacetime]; Morfa-Morales JMP(11)-a1105 [on de Sitter spacetimes].
@ Fractal spacetime: Eyink CMP(89), CMP(89); Calcagni JHEP(10)-a1001 [power-counting renormalizable theory]; Kar & Rajeev AP(12)-a1110; > s.a. fractals in physics.
@ Other generalized background: Kaiser AP(87) [complex spacetime]; Birmingham & Rakowski MPLA(94) [simplicial complex, intersection form action]; White et al CQG(10)-a0812 [signature-changing]; Weinfurtner et al JPCS(09)-a0905 [in analog gravity]; Meljanac et al a1701, Mignemi a1911-conf [generalized Snyder spaces].
@ With fundamental length scale: Brüning & Nagamachi JMP(04) [in terms of ultra-hyperfunctions]; Hossenfelder CQG(08)-a0712; Soloviev JMP(09)-a0912, JMP(10)-a1012.
@ Discrete: Kur'yan in(91) [discrete spacetime]; Norton & Jaroszkiewicz JPA(98) [discrete time]; Häußling AP(02) [and non-commutative geometry]; Gudder a1704; > s.a. quantum field theory on graphs.
> Related topics: see fractional calculus; non-standard analysis; quantum field theory states [including non-equilibrium].

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