Axiomatic formulations of nonlocal and noncommutative field theories

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 by that with the light wedge. We explain some essential peculiarities of deriving the CPT and spin-statistics theorems in this enlarged framework.

LaTeX, 13 pages, no figures

References in corpus (2)

• PCT, spin and statistics, and analytic wave front set
• Carrier cones of analytic functionals

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• Twisted convolution and Moyal star product of generalized functions
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• The Hierarchy Problem: From the Fundamentals to the Frontiers
• Towards an Axiomatic Formulation of Noncommutative Quantum Field Theory. II