Quantum Field Theory – Types of Theories| 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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