Axiomatic formulations of nonlocal and noncommutative field theories
Teoretičeskaâ i matematičeskaâ fizika, Tome 147 (2006) no. 2, pp. 257-269
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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.
@article{TMF_2006_147_2_a3,
author = {M. A. Soloviev},
title = {Axiomatic formulations of nonlocal and noncommutative field theories},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {257--269},
publisher = {mathdoc},
volume = {147},
number = {2},
year = {2006},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2006_147_2_a3/}
}
M. A. Soloviev. Axiomatic formulations of nonlocal and noncommutative field theories. Teoretičeskaâ i matematičeskaâ fizika, Tome 147 (2006) no. 2, pp. 257-269. http://geodesic.mathdoc.fr/item/TMF_2006_147_2_a3/