Local Wick Polynomials and Time Ordered Products¶of Quantum Fields in Curved Spacetime
By S. Hollands, R. Wald. 2001
442 citations recorded by the source corpus.
Abstract: In order to have well defined rules for the perturbative calculation of quantities of interest in an interacting quantum field theory in curved spacetime, it is necessary to construct Wick polynomials and their time ordered products for the noninteracting theory. A construction of these quantities has recently been given by Brunetti, Fredenhagen, and Köhler, and by Brunetti and Fredenhagen, but they did not impose any “locality” or “covariance” condition in their constructions. As a consequence, their construction of time ordered products contained ambiguities involving arbitrary functions of spacetime point rather than arbitrary parameters. In this paper, we construct an “extended Wick polynomial algebra”– large enough to contain the Wick polynomials and their time ordered products – by generalizing a construction of Dütsch and Fredenhagen to curved spacetime. We then define the notion of a local, covariant quantum field, and seek a definition of local Wick polynomials and their time ordered products as local, covariant quantum fields. We introduce a new notion of the scaling behavior of a local, covariant quantum field, and impose scaling requirements on our local Wick polynomials and their time ordered products as well as certain additional requirements – such as commutation relations with the free field and appropriate continuity properties under variations of the spacetime metric. For a given polynomial order in powers of the field, we prove that these conditions uniquely determine the local Wick polynomials and their time ordered products up to a finite number of parameters. (These parameters correspond to the usual renormalization ambiguities occurring in Minkowski spacetime together with additional parameters corresponding to the coupling of the field to curvature.) We also prove existence of local Wick polynomials. However, the issue of existence of local time ordered products is deferred to a future investigation.
Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/87af15ed3fa749eb8c10ef8f4c4e50f03e87f208
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Citations in the corpus
- Existence of Local Covariant Time Ordered Products of Quantum Fields in Curved Spacetime (2001, methodology): “These requirements are the ones previously given in [12] except that we have replaced the continuity requirement of [12] under smooth variations of the metric with a smoothness requirement.”
- Axiomatic Quantum Field Theory in Curved Spacetime (2008, background): “This idea may be formulated in a precise manner as follows [19, 20, 7].”
- 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].”
- Batalin-Vilkovisky Formalism in Perturbative Algebraic Quantum Field Theory (2011, methodology): “We use the fact that from the construction performed in [39] follows that T 1 is a functor from F loc to A loc .”
- Renormalized Quantum Yang-Mills Fields in Curved Spacetime (2007, unknown): “311 of [62], it suffices to cons ider a suitable analytic family of linear functionals onW0 that do not necessarily satisfy the positivity condition re quired for states.”
- Infrared effects in inflationary correlation functions (2010, unknown): “A manifestly local and covariant formulation of this expansion in curved spacetime has been given by Hollands and Wald [112–116], which in principle could be applied to the study of infrared effects in nearly de Sitter spacetimes.”
- Algebraic QFT in Curved Spacetime and Quasifree Hadamard States: An Introduction (2014, methodology): “A full classification of them is the first step of ultraviolet renormalization program [36, 45].”
- Perturbative Algebraic Quantum Field Theory and the Renormalization Groups (2009, unknown): “After this breakthrough, a thorough construction of renormalized perturbative quantum field theory on generic curved spacetimes could successfully be performed [5, 25, 26, 28] in the framework of Algebraic Quantum Field Theory.”