Existence of Local Covariant Time Ordered Products of Quantum Fields in Curved Spacetime
By S. Hollands, R. Wald. 2001
353 citations recorded by the source corpus.
Abstract: We establish the existence of local, covariant time ordered products of local Wick polynomials for a free scalar field in curved spacetime. Our time ordered products satisfy all of the hypotheses of our previous uniqueness theorem, so our construction essentially completes the analysis of the existence, uniqueness, and renormalizability of the perturbative expansion for nonlinear quantum field theories in curved spacetime. As a byproduct of our analysis, we derive a scaling expansion of the time ordered products about the total diagonal that expresses them as a sum of products of polynomials in the curvature times Lorentz invariant distributions, plus a remainder term of arbitrarily low scaling degree.
Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/2c1b76208921f994ecf919d30d5865cf716ddb14
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In Mathematical Physics
In Nuclear and High Energy Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Boundary conditions and dualities: vector fields in AdS/CFT (2006, background): “Any such setting leads to a well-defined (though not necessarily renormalizable) framework for perturbative quantization [28, 42, 43].”
- The Spin-Foam Approach to Quantum Gravity (2012, background): “In fact by taking special care in the mathematical definition of the products of distributions at the same point, in good cases, one can provide a definition of the quantum theory, which is completely free of UV divergences [171] (see also [343, 224, 225]).”
- Algebraic QFT in Curved Spacetime and Quasifree Hadamard States: An Introduction (2014, background): “The algebra W(M) also includes the so-called (locally covariant) time-ordered Wick polynomials, necessary to completely perform the renormalization procedure [37].”
- Axiomatic Quantum Field Theory in Curved Spacetime (2008, methodology): “This idea may be formulated in a precise manner as follows [19, 20, 7].”
- Conservation of the Stress Tensor in Perturbative Interacting Quantum Field Theory in Curved Spacetimes (2004, methodology): “In [14], we imposed a list of requirements on time-ordered products.”
- Perturbative Algebraic Quantum Field Theory and the Renormalization Groups (2009, neutral): “(70)The one parameter group (Ẑ(ρ))ρ>0 was found by Hollands and Wald [27℄.”
- Renormalized Quantum Yang-Mills Fields in Curved Spacetime (2007, neutral): “Such a scheme was found in [62, 63] for interacting scalar field theory, based on key earlier work of [18, 17], and also on the w ork [37, 38], where an algebraic variant of perturbation theory in flat space was developed.”