Covariant Quantum Gravity| Covariant Quantum Gravity |
In General > s.a. effective
quantum field theory; perturbations in general relativity.
* Idea: A perturbative
approach to quantum gravity, similar to those of other field theories,
which focuses on scattering processes involving gravitons; The name refers
to Poincaré covariance with respect to the Minkowski background.
* Procedure: One chooses a
background metric η, usually Minkowski, divides the physical
metric into 2 terms, gab
= ηab
+ G1/2hab
(hab = "gravitational
potential"), and treats this as an interacting spin-2 field theory
(G1/2 here really is lP,
that's where it appears); To calculate amplitudes, use the Lorentzian path-integral approach (with the Faddeev-Popov
trick) and the stationary-phase (saddle-point) approximation; For general relativity, the partition function is
Z[gc, j] = ∫ \(\cal D\)h \(\cal D\)φ exp{(i/\(\hbar\)) ∫ G−1 |g|1/2 [R(g)−Λ] + \(\cal L\)(φ, g, j)} ;
To generate 1-loop diagrams, expand to second order; The external lines
are on shell iff η satisfies the Einstein equation.
* Motivation: It is a
pragmatic approach in which one knows how to do certain things without
the need for a new framework, and it should work if one stays well above
the Planck length; It is unitary [@ DeWitt].
* Drawbacks: (1) Not a deep
approach, misses many features that distinguish quantum gravity from other
field theories; (2) Linearized approach, which uses a fixed background; (3)
The resulting quantum field theory appears to be non-renormalizable [@ 't Hooft
& Veltman AIHP(74), ...], although some ways of
overcoming this problem have been proposed; (4) The semiclassical ground state
is unstable [@ Horowitz, Hartle]; (5) It cannot address questions related to
the regime near the initial singularity; (6) One does not know what the path
integral measure is, nor how to give a covariant meaning to \(\langle h,
t \mid h', t' \rangle\).
Issues and Techniques
> s.a. approaches [perturbative]; graviton [production,
propagator, scattering]; renormalization; semiclassical
general relativity.
* Stability of Minkowski: Flat
spacetime cannot decay, because of the positive-energy theorem, but it can
have large fluctuations.
* Graviton propagator: One-loop
corrections to it induce 1/r3
corrections to the Newtonian gravitational potential.
* With cosmological constant: The theory with
a massive graviton has discontinuities at m2 →
0 (5 \(\mapsto\) 2 degrees of freedom) and (2/3) Λ (5 \(\mapsto\) 4 degrees of freedom).
@ Around Minkowski: Brout et al PRL(79),
NPB(80) [zero point energy and cosmological constant];
Modanese NPB(00) [dipole fluctuations];
de Berredo-Peixoto et al MPLA(00)gq/01 [1-loop calculation].
@ Stability of Minkowski:
Hartle & Horowitz PRD(81);
Horowitz in(81);
Gunzig et al PLB(90);
Mazzitelli & Rodrigues PLB(90) [with R2 term];
Simon PRD(91);
Garattini IJMPA(99)gq/98 [foamy];
Modanese PLB(99)gq.
@ Other spacetimes: Gross et al PRD(82) [Schwarzschild, T ≠ 0];
Tsamis & Woodard CQG(90),
CMP(94);
Forgacs & Niedermaier ht/02,
Niedermaier JHEP(02)ht [2-Killing-vector-field reduction, renormalization];
Christiansen et al PRD(18)-a1711 [constant-curvature backgrounds].
@ With coupled matter: Mackay & Toms PLB(10)-a0910 [scalar, Vilkovisky-DeWitt effective action];
> s.a. matter phenomenology.
@ Excitations in general:
Chapline CSF(99)-ht/98 [branes and conformal gravity].
@ Infrared behavior:
Antoniadis et al PLB(94) [scale invariance];
Tsamis & Woodard AP(95) [strong infrared effects];
Ware et al JHEP(13)-a1308 [asymptotic S matrix];
Wetterich PRD(18)-a1802;
> s.a. 3D quantum gravity; matter phenomenology.
@ Ultraviolet behavior:
Korepin a0905 [one-loop cancellation of UV divergences];
Christiansen et al PRD(15)-a1506 [functional renormalisation group approach];
Deser GRG(16)-a1609 [in D > 4 not all 1-loop divergences can be removed];
Anselmi & Piva JHEP(18)-a1803.
@ Related topics: Donoghue & Torma PRD(96) [loop diagrams];
Grigore CQG(00)ht/99 [and ghosts];
Bern et al PRL(00)ht/99 [strings and graviton-matter coupling];
Dilkes et al PRL(01)ht,
Duff et al PLB(01)ht
[mg → 0 and (2/3) Λ discontinuities];
Datta et al PLB(04)hp/03 [angular momentum selection rules];
Bjerrum-Bohr et al JHEP(10)-a1005 [Kawai-Lewellen-Tye relations to gauge-theory amplitudes];
Ohta et al JHEP(16)-a1605 [off-shell one-loop divergences, and unimodular gravity];
Rafie-Zinedine a1808-MS [simplified Feynman rules];
Abreu et al PRL(20)-a2002
[two-loop four-graviton scattering amplitudes].
> Other: see higher-order and other modified
theories [linearized, and propagator]; tests of general relativity.
References > s.a. quantum gravity
/ canonical [relationship]; quantum cosmology.
@ General: DeWitt PR(67),
PR(67);
DeWitt in(72);
Faddeev & Popov SPU(73);
Duff in(75);
Ward a0810-conf [status and update];
Hodges a1108
[tree-level gravitational scattering amplitudes];
Jakobsen a2010-MSc
[classical general relativity is derived from quantum field theory].
@ Boundary conditions: Avramidi & Esposito CQG(98)ht/97,
ht/97-GRF;
Esposito IJMPA(00)gq [boundary operators].
@ Corrections to classical theory: Iliopoulos et al NPB(98) [on spatially flat FLRW models];
Gibbons CQG(99)ht;
Khriplovich & Kirilin JETP(04)gq/04.
@ Relationship with gauge theory: Bern et al NPB(99)gq/98;
Bern LRR(02)gq;
Bjerrum-Bohr et al JHEP(10)-a1007 [and Yang-Mills amplitudes, tree level];
Bern et al PRD(10)-a1004 [as the "square of gauge theory"].
@ Other relationships: Baryshev Grav(96)gq/99 [vs geometrodynamics];
Bern ht/01-conf [and string theory];
Mattei et al NPB(06)gq/05 [and path integrals/spin-foams].
@ Causal perturbation theory: Grillo ht/99,
ht/99,
ht/99;
Grillo AP(01)ht/99 [and scalar matter];
Wellmann PhD(01)ht [spin-2 quantum gauge theory];
Grigore CQG(10)-a1002 [second-order, conditions on interactions with matter].
@ Related theories: Hamada PTP(00)ht/99 [2-loop renormalizable];
Bell et al gq/00-proc ["versatile"];
Nojiri & Odintsov PLB(10) [renormalizable];
Tessarotto & Cremaschini Ent(18)-a1807 [Generalized Lagrangian Path approach].
@ Related topics: Boulware & Deser AP(75) [and classical general relativity];
Tsamis & Woodard AP(92) [Green functions];
Modesto GRG(05)ht/03 [bosonic tensor fields].
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 11 may 2021