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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