zbMATH — the first resource for mathematics

Local and gauge invariant observables in gravity. (English) Zbl 1327.83125

83C47 Methods of quantum field theory in general relativity and gravitational theory
81T20 Quantum field theory on curved space or space-time backgrounds
81P15 Quantum measurement theory, state operations, state preparations
53Z05 Applications of differential geometry to physics
81T13 Yang-Mills and other gauge theories in quantum field theory
Full Text: DOI arXiv
[1] Barnich G, Brandt F and Henneaux M 2000 Local BRST cohomology in gauge theories 338 439–569 Phys. Rep. · Zbl 1097.81571
[2] Bergmann P and Komar A 1960 Poisson brackets between locally defined observables in general relativity Phys. Rev. Lett.4 432–3
[3] Bergmann P G 1961 Observables in general relativity Rev. Mod. Phys.33 510–4 · Zbl 0098.42501
[4] Bonga B and Khavkine I 2014 Quantum astrometric observables: II. Time delay in linearized quantum gravity Phys. Rev. D 89 024039
[5] Borgman J and Ford L H 2004 Effects of stress tensor fluctuations upon focusing Phys. Rev. D 70 064032
[6] Brunetti R and Fredenhagen K 2009 Quantum field theory on curved backgrounds Quantum Field Theory on Curved Spacetimes: Concepts and Method (Lecture Notes in Physics vol 786) ed C Bär and K Fredenhagen (Berlin: Springer) · Zbl 1184.81099
[7] Brunetti R, Fredenhagen K and Rejzner K 2013 Quantum gravity from the point of view of locally covariant quantum field theory http://arxiv.org/abs/1306.1058v4 · Zbl 1346.83001
[8] Brunetti R, Fredenhagen K and Ribeiro P L 2012 Algebraic structure of classical field theory: I. Kinematics and linearized dynamics for real scalar fields http://arxiv.org/abs/1209.2148
[9] Christodoulou D and Klainerman S 1993 The global nonlinear stability of the Minkowski space Princeton Mathematical Series vol 41 (Princeton, NJ: Princeton University Press) · Zbl 0827.53055
[10] Coley A, Hervik S and Pelavas N 2009 Spacetimes characterized by their scalar curvature invariants Class. Quantum Grav.26 025013 · Zbl 1158.83023
[11] Coley A, Hervik S and Pelavas N 2010 Lorentzian manifolds and scalar curvature invariants Class. Quantum Grav.27 102001 · Zbl 1190.83023
[12] DeWitt B S 1963 The quantization of geometry Gravitation: An Introduction to Current Research ed L Witten (New York: Wiley) ch 8 pp 266–381
[13] Fewster C J and Hunt D S 2013 Quantization of linearized gravity in cosmological vacuum spacetimes Rev. Math. Phys.25 1330003 · Zbl 1266.83024
[14] Ford L H 1995 Gravitons and light cone fluctuations Phys. Rev. D 51 1692
[15] Fredenhagen K and Rejzner K 2012 Batalin–Vilkovisky formalism in the functional approach to classical field theory Commun. Math. Phys.314 93–127 · Zbl 1418.70034
[16] Giddings S, Marolf D and Hartle J 2006 Observables in effective gravity Phys. Rev. D 74 064018
[17] Gordillo A, Navarro J and Sancho J B 2009 Moduli spaces for finite-order jets of Riemannian metrics Differ. Geom. Appl.28 672–88 · Zbl 1202.58008
[18] Hack T-P and Schenkel A 2013 Linear bosonic and fermionic quantum gauge theories on curved spacetimes Gen. Relativ. Gravit.45 877–910 · Zbl 1269.83037
[19] Hervik S and Coley A 2010 Curvature operators and scalar curvature invariants Class. Quantum Grav.27 095014 · Zbl 1190.83087
[20] Hirsch M W 1976 Differential topology (Graduate Texts in Mathematics vol 33) (Berlin: Springer)
[21] Khavkine I 2012 Characteristics, conal geometry and causality in locally covariant field theory http://arxiv.org/abs/1211.1914
[22] Khavkine I 2012 Quantum astrometric observables: time delay in classical and quantum gravity Phys. Rev. D 85 124014
[23] Khavkine I 2014 Covariant phase space, constraints, gauge and the Peierls formula Int. J. Mod. Phys. A 29 1430009 · Zbl 1284.70003
[24] Kriegl A and Michor P W 1997 The convenient setting of global analysis Mathematical Surveys and Monographs vol 53 (Providence, RI: American Mathematical Society) · Zbl 0889.58001
[25] Kruglikov B and Lychagin V 2015 Global Lie–Tresse theorem http://arxiv.org/abs/1111.5480v3
[26] Krupka D and Janyška J 1990 Lectures on Differential Invariants (Brno: Universita J.E. Purkyně)
[27] Ohlmeyer S 1997 The measurement of length in linear quantum gravity PhD Thesis DESY, Hamburg http://unith.desy.de/research/aqft/doctoral_theses/
[28] Olver P J 1993 Applications of lie groups to differential equations Graduate Texts in Mathematics vol 107 (New York: Springer) 2nd edn · Zbl 0785.58003
[29] Olver P J 1999 Classical Invariant Theory London Mathematical Society Student Texts vol 44 2nd edn (Cambridge: Cambridge University Press)
[30] Olver P J and Pohjanpelto J 2009 Differential invariant algebras of Lie pseudo-groups Adv. Math.222 1746–92 · Zbl 1194.58018
[31] Rejzner K 2011 Batalin–Vilkovisky formalism in locally covariant field theory PhD Thesis Hamburg arXiv:1111.5130
[32] Sharapov A A 2014 Peierls brackets in non-Lagrangian field theory Int. J. Mod. Phys. A 29 1450157 · Zbl 1303.70025
[33] Stephani H, Kramer D, MacCallum M, Hoenselaers C and Herlt E 2003 Exact Solutions of Einstein’s Field Equations (Cambridge: Cambridge University Press) · Zbl 1057.83004
[34] Tambornino J 2012 Relational observables in gravity: a review Symmetry Integr. Geom.: Methods Appl.8 017 · Zbl 1242.83047
[35] Thompson R T and Ford L H 2006 Spectral line broadening and angular blurring due to spacetime geometry fluctuations Phys. Rev. D 74 024012
[36] Tsamis N C and Woodard R P 1992 Physical Green’s functions in quantum gravity Ann. Phys., NY215 96–155
[37] Wockel C 2009 A generalisation of Steenrod’s approximation theorem Archivum Mathematicum pp 9–104 (Brno) arXiv:math/0610252
[38] Woodard R P 1984 Invariant formulation of and radiative corrections in quantum gravity PhD Thesis Harvard University, Cambridge, MA
[39] Yu H and Ford L H 1999 Light-cone fluctuations in flat spacetimes with nontrivial topology Phys. Rev. D 60 084023
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.