This article is cited in 15 papers

Axiomatic formulations of nonlocal and noncommutative field theories

M. A. Soloviev

P. N. Lebedev Physical Institute, Russian Academy of Sciences

Abstract: We analyze functional analytic aspects of axiomatic formulations of nonlocal and noncommutative quantum field theories. In particular, we completely clarify the relation between the asymptotic commutativity condition, which ensures the CPT symmetry and the standard spin–statistics relation for nonlocal fields, and the regularity properties of the retarded Green's functions in momentum space that are required for constructing a scattering theory and deriving reduction formulas. This result is based on a relevant Paley–Wiener–Schwartz-type theorem for analytic functionals. We also discuss the possibility of using analytic test functions to extend the Wightman axioms to noncommutative field theory, where the causal structure with the light cone is replaced with that with the light wedge. We explain some essential peculiarities of deriving the CPT and spin–statistics theorems in this enlarged framework.

Keywords: nonlocal quantum fields, causality, noncommutative field theory, Wightman functions, analytic functionals, Paley–Wiener–Schwartz theorem.

Received: 28.10.2005

DOI: 10.4213/tmf1962

 English version: Theoretical and Mathematical Physics, 2006, 147:2, 660–669

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