Quantum Field Theory – Types of Theories  

In General > s.a. generalized theories [including non-local, deformed, and theories with a fundamental length]; types of fields [including polymer].
* Free vs interacting: A field is free if the representation describing a many-particle system is the tensor product of the corresponding single-particle representations.
@ General references: Lev JPA(99)qp/98; Ratsimbarison a0706/FizB [construction of probabilistic theories]; Dereziński JMP(14)-a1307 [with classical interactions]; Weinberg a2010 [allowed massless particles described by tensor and spinor-tensor fields].
@ Scalar theories (spin-0): Harrivel mp/06 [perturbative expansion]; Gielerak a1803 [not quasi-free, obeying all Wightman axioms]; > s.a. klein-gordon theory.
@ Vector theories (spin-1): Blommaert et al JHEP(18)-a1801 [entanglement structure]; > s.a. quantum gauge theories and QED.
@ 0+1: Boozer EJP(07) [as toy model].
@ 1+1: Dereziński & Meissner LNP(06)mp/04 [massless]; Schroer ht/05-en [rev], AP(06)ht/05 [as testing ground]; Dorey et al ed-JPA(06) [low-dimensional]; Falco a1208-conf [and applications to statistical mechanics]; Iraso & Mnev CMP(19)-a1806 [Yang-Mills theories with corners].
@ 2+1: Robinson et al JMP(09)-a0903 [spin-1/2 symplectic fermions].
@ Space of quantum field theories: Douglas a1005; Balasubramanian et al a1410 [relative entropy and proximity of quantum field theories].

Diffeomorphism-Invariant or Background-Independent Theories > s.a. algebraic and axiomatic approaches; parametrized theories.
* Locally covariant quantum field theory: A theory is described as a functor from a category of spacetimes to a category of *-algebras; > s.a. gauge groups.
@ General references: Fredenhagen & Haag CMP(87); Kuchař in(88); Horowitz CMP(89) [exactly soluble]; Rovelli NPB(93), JMP(95)gq [and model for quantum geometry]; Thiemann gq/93, CQG(95)gq/99; Salehi IJTP(97) [dynamics formalism]; Baez & Krasnov JMP(98) [with fermions]; Conrady et al PRD(04) [vacuum]; Fredenhagen ht/04-proc; Dreyer ht/04; Balachandran et al IJMPA(09)ht/06 [on the Groenewold-Moyal plane]; Campiglia et al PRD(06)gq [uniform discretizations]; Pinamonti CMP(09) [conformally invariant]; Neiman CQG(09)-a0901 [degrees of freedom over finite spatial regions]; Rovelli JPCS(11)-a1010 [simple quantum gravity model].
@ Parametrized theories: Laddha & Varadarajan PRD(08)-a0805, PRD(11)-a1011 [2D scalar, as model for 4D gravity]; Sengupta CQG(14) + CQG+(14) [2D, asymptotically flat scalar].
@ Locally covariant: Fewster & Verch AHP(12)-a1106, Fewster PTRS(15)-a1502 [and "the same physics in all spacetimes"]; Fewster & Schenkel AHP(14)- a1402 [with external sources]; > s.a. approaches to quantum gravity; renormalization.
@ Scalar fields: Husain PRD(93)gq [and loop-based observables]; Varadarajan PRD(04)gq [path integral]; Sahlmann CQG(07)gq/06 [diffeomorphism-invariant Hilbert space].
> Specific types: see quantum gauge theories and QED; quantum gravity; topological theories.

Other Types of Theories > s.a. boundaries in field theory; discrete spacetime; quantum field theory in curved spacetime [including scalar, spin-1, spin-3/2].
@ Exactly solvable theories: Ushveridze MPLA(98) [quasi-exactly solvable]; Brodsky et al AP(02) [and Pauli-Villars fields].
@ Coupled to atoms: Hu & Raval qp/97; Retamal et al PLA(06) [entanglement]; > s.a. Dicke Model; Friedrichs Model.
@ Coupled to atoms, finite T: Sowiński a0901; Khanna et al PRA(10)-a0910 [thermal effects, and stability].
@ Theories with S unbounded below: Greensite & Halpern NPB(84) [Euclidean quantum theory]; Zavialov et al TMP(96).
@ UV-finite theories: Lemes et al JPA(01) [criterion]; Moffat a1104 [gauge invariance in UV-complete theories].
@ Ultralocal theories: Klauder CMP(70), APA(71) [quantization]; Klauder JPA(01)qp/00 [and reparametrization-invariant]; Varadarajan CQG(17)-a1609 [and propagation]; Klauder a2007 [quantum gravity].
@ Non-Lagrangian theories: in Kaparulin JMP(10)-a1001 [Lagrange-anchor construction].
@ Group field theories: Gurau CMP(11)-a0912 [fermionic, with color symmetry]; Rivasseau a1209-conf [tensor group feld theories]; Krajewski a1210-ln; Oriti a1211-proc [quantum geometry]; Baratin et al PRD(14)-a1405 [modification]; Kegeles et al CQG(18)-a1709 [inequivalent coherent state representations]; > s.a. approaches to quantum gravity; renormalization.
@ Other types of theories: Segal JMP(60), JMP(64) [non-linear]; Grigore JMP(95) [free]; Chalmers JHEP(98)ht/97 [non-polynomial]; Maiani & Testa AP(98) [unstable]; Brouder ht/03 [degenerate systems]; Benini et al AHP(13)-a1210 [bosonic and fermionic field theories on affine bundles]; Freed & Teleman CMP(14)-a1212 [relative quantum field theory]; Strauss et al a1407 [classically unstable]; Underwood & Valentini PRD(15)-a1409 [relic non-equilibrium systems]; Barbero et al CQG(15)-a1501 [coupled to point masses]; Aashish & Panda PRD(18)-a1803 [rank-2 antisymmetric fields, effective action approach]; Runkel & Szegedy a1807 [area-dependent theories, with defects]; > s.a. conformal invariance; integrable theories; momentum [in curved momentum space].
> Specific types: see composite systems; effective actions; Lifshitz-Type Theories; many-particle quantum systems; supersymmetric field theory.

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