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.
60 pages, Latex, 6 figures in EPS-format, v2: added sec. 8 and sec. 9, streamlined sec. 10, typos corrected, references added
References in corpus (4)
- The operator product expansion for perturbative quantum field theory in curved spacetime
- Vertex Algebras in Higher Dimensions and Globally Conformal Invariant Quantum Field Theory
- Partial wave expansion and Wightman positivity in conformal field theory
- Harmonic bilocal fields generated by globally conformal invariant scalar fields