Quantum Field Theory in Curved Spacetime |
In General > s.a. effective theories.
* Idea: A theory in which matter fields
are quantized but the spacetime metric acts as a fixed background; It is not thought
of as a fundamental theory, but is useful in the study of specific effects.
* History: Precursor work was done by
Schrödinger in the 1930s, but the field was really started by Bryce DeWitt, and in
the cosmological context by a 1969-1971 series of papers by Leonard Parker on particle
creation in an expanding universe; It received a bigger impetus after Hawking's work
on black-hole radiation.
* Approaches: Quantum field theory in
curved spacetime may be defined either through a manifestly unitary canonical approach,
or via the manifestly covariant path integral formalism; For gauge theories, these two
approaches have produced conflicting results.
* Difficulty with unitarity: In general
there may be no unitary evolution between states defined on two arbitrary Cauchy surfaces,
even in Minkowski spacetime–but one must remember that a general dieomorphism is
not a symmetry of the theory; However, > see QED
in curved spacetime.
* Other difficulties: There is no canonical
definition of ω > 0 modes and particles (no Poincaré invariance);
This issue has been solved only for stationary cases or in/out states (S-matrix) in
asymptotically flat cases; Can generalize only fields with s ≥ 1; Only the
linear case is understood.
@ Unitarity of evolution:
Friedman et al PRD(92);
Torre & Varadarajan CQG(99);
Colosi & Oeckl ONPPJ(11)-a0912;
Agulló & Ashtekar PRD(15)-a1503 [generalized notion];
> s.a. different backgrounds.
@ Limitations: Parentani gq/97-proc [validity];
Giddings PRD(07)ht [black-hole background];
> s.a. semiclassical gravity [including corrections to gravity].
@ Related topics: Singh & Mobed AdP(10)-a0902 [breakdown of Casimir invariance];
Yao a0907/FP [arbitrary observer];
Kleinert EJTP(09)-a0910 [quantization in the neighborhood of a point];
Fredenhagen & Hack a1308 [and phenomenological applications to cosmology].
Covariant Quantization
* Idea: Look for a set of
field operators φ(x) satisfying Heisenberg's equations
of motion and the commutation relations (e.g. for a scalar field):
[φ(x), φ(y)] = − i\(\hbar\) G(x, y) , where G is such that φ(y) = ∫Σ G(y, x) (←∂a − ∂a→) φ(x) dσa ;
If M is globally hyperbolic, G exists and is unique.
Other Approaches > s.a. algebraic and axiomatic approach;
geometric quantization; path-integral approach.
@ Canonical: Fulling PRD(73) [ambiguity];
Wyrozumski PRD(90) [fiber bundle formalism];
Calixto et al IJMPA(00)ht/97 [group quantization];
Corichi et al PRD(02)gq,
CQG(03)gq/02,
AP(04)ht/02 [scalar field, Schrödinger, Fock, and algebraic];
Moschella & Schaeffer JCAP(09)-a0802,
AIP(09)-a0904 [new formulation];
Cortez et al JCAP(10)-a1004 [unique Fock quantization];
> s.a. Proca Theory.
@ Geometric quantization:
Woodhouse RPMP(77);
Kalinowski & Piechocki IJMPA(99).
@ Other states: Buchholz RVMP(00)mp/98 [from spacetime transformations];
Oeckl PLB(05)ht [on timelike hypersurfaces];
> s.a. thermal states.
@ Correlation dynamics, statistical aspects: Wald in(93) [cosmology, and horizons];
Hu gq/95 [and black-hole information];
> s.a. correlations.
@ Histories approach: Blencowe AP(91);
Anastopoulos JMP(00)gq/99 [time-dependent Hilbert space].
@ Operator product expansion: Hollands & Wald GRG(08)-a0805.
Techniques > s.a. complex structure;
formalism and techniques; green functions [propagator];
Hadamard States; regularization.
@ Renormalization:
Castagnino et al PRD(86) [Hadamard and minimal compared];
Buchbinder et al RNC(89);
Hollands & Wald CMP(03)gq/02 [scalar];
Banks & Mannelli PRD(03)ht/02 [in de Sitter space];
Shapiro CQG(08)-a0801 [semiclassical, pedagogical];
Casadio JPCS(09)-a0902 ["gravitational"];
Barceló et al PRD(12) [equivalence between two different renormalized stress-energy tensors];
Viet Dang a1312 [causal approach].
@ Related topics: Habib & Kandrup AP(89) [density matrix and Wigner functions];
Prugovečki CQG(96) [Hilbert bundles on spacetime];
Antonsen PRD(97)ht [from Wigner function];
Mashkevich gq/98,
gq/98 [alternative approach];
Hollands & Wald CMP(01)gq,
RVMP(05)gq/04
[conditions on Wick polynomials and Tab conservation];
Doukas et al CQG(15)-a1306 [discriminating quantum field theories in curved spacetime];
Gérard a1901 [microlocal analysis methods];
> s.a. Foldy-Wouthuysen Representation.
Theories > s.a. various backgrounds and
effects; non-commutative field theory.
@ Scalar field: Haba JPA(02)ht [λφ4 in scale-invariant quantum metric];
Gibbons et al a1907 [higher-derivative scalar field];
Ribeiro & Shapiro JHEP(19)-a1908
[light scalar field coupled to much more massive one, effective theory];
> s.a. klein-gordon fields.
@ Scalar field, renormalization: Tichy & Flanagan PRD(98)gq;
Décanini & Folacci PRD(08)gq/05 [Hadamard, arbitrary dimensionality].
@ Scalar field, semiclassical:
Camblong & Ordóñez PRD(05) [and black-hole thermodynamics];
Grain & Barrau NPB(06)ht [WKB approach];
Grain & Barrau PRD(07) [propagator, pedagogical].
@ Spin-1 field: Buchbinder et al PRD(17)-a1703 [non-minimally coupled massive, effective action];
> s.a. generalized theories [non-local]; Proca Theory.
@ Other theories:
Pahlavan & Bahari IJTP(09),
Takook et al EPJC(12)-a1206 [spin-3/2 fields, in de Sitter space];
Bilić et al PLB(12)-a1110 [supersymmetric model];
de Medeiros & Hollands CQG(13)-a1305 [superconformal];
> s.a. dirac fields; quantum gauge theories.
References
> s.a. entropy bound and quantum entropy;
particle effects [creation, including early universe].
@ Simple: Polarski Rech(90).
@ General: Choquet-Bruhat in(68);
Hájíček in(77),
PRD(77);
Horowitz & Wald PRD(78);
Birrell & Taylor JMP(78);
Fulling GRG(79);
Wald AP(79) [S-matrix];
Ashtekar & Magnon GRG(80);
Kibble & Randjbar-Daemi JPA(80);
Kay in(82);
Martellini NCA(82),
CQG(84);
Haag et al CMP(84);
Brunetti & Fredenhagen LNP(09)-a0901;
Stoyanovsky a0910 [mathematical definition];
Baer & Ginoux SPM(12)-a1104;
Fewster & Liberati GRG(14)-a1402 [GR20 report];
Benini & Dappiaggi a1505 [three explicit examples];
Barbado et al EPJC(20)-a1811 [method for computing the evolution];
Colosi & Oeckl PRD(19)-a1903 [generalized
notion of vacuum and amplitude admitting a localization in spacetime regions and on hypersurfaces].
@ Textbooks: Birrell & Davies 84;
Kay in(88);
Fulling 89;
Wald 94;
Mukhanov & Winitzki 07;
Parker & Toms 09.
@ Reviews: DeWitt RMP(57),
PRP(75);
Isham in(77);
Parker in(77),
in(79);
Gibbons in(79);
Davies in(80);
Birrell in(81);
Duff in(81);
Hu in(82);
Wald in(95),
gq/95-GR14,
gq/98-in;
Ford gq/97-proc;
Liberati PhD(00)gq [vacuum effects];
Jacobson gq/03-ln;
Kay in(06)gq;
Wald gq/06-conf [history and status],
a0907-proc;
Haro a1011-ln;
Benini et al IJMPA(13)-a1306 [primer];
Hollands & Wald PRP(15)-a1401;
Fredenhagen & Rejzner JMP(16)-a1412 [framework and examples];
Miao et al a1505-in [non-technical].
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