Quantum field theory in terms of consistency conditions I: General framework, and perturbation theory via Hochschild cohomology
arXiv:0802.2198
Abstract
In this paper, we propose a new framework for quantum field theory in terms of consistency conditions. The consistency conditions that we consider are "associativity" or "factorization" conditions on the operator product expansion (OPE) of the theory, and are proposed to be the defining property of any quantum field theory. Our framework is presented in the Euclidean setting, and is applicable in principle to any quantum field theory, including non-conformal ones. In our framework, we obtain a characterization of perturbations of a given quantum field theory in terms of a certain cohomology ring of Hochschild-type. We illustrate our framework by the free field, but our constructions are general and apply also to interacting quantum field theories. For such theories, we propose a new scheme to construct the OPE which is based on the use of non-linear quantized field equations.
arXiv comment60 pages, Latex, 6 figures in EPS-format, v2: added sec. 8 and sec. 9, streamlined sec. 10, typos corrected, references added
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Cited by in corpus (6)
- Action principle for OPE
- Recursive construction of operator product expansion coefficients
- Operator product expansion algebra
- Perturbative Quantum Field Theory via Vertex Algebras
- All-order existence of and recursion relations for the operator product expansion in Yang-Mills theory
- Local Commutators and Deformations in Conformal Chiral Quantum Field Theories