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Teoreticheskaya i Matematicheskaya Fizika, 2006, Volume 147, Number 2, Pages 257–269
DOI: https://doi.org/10.4213/tmf1962
(Mi tmf1962)
 

This article is cited in 15 scientific papers (total in 15 papers)

Axiomatic formulations of nonlocal and noncommutative field theories

M. A. Soloviev

P. N. Lebedev Physical Institute, Russian Academy of Sciences
References:
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
English version:
Theoretical and Mathematical Physics, 2006, Volume 147, Issue 2, Pages 660–669
DOI: https://doi.org/10.1007/s11232-006-0068-7
Bibliographic databases:
Language: Russian
Citation: M. A. Soloviev, “Axiomatic formulations of nonlocal and noncommutative field theories”, TMF, 147:2 (2006), 257–269; Theoret. and Math. Phys., 147:2 (2006), 660–669
Citation in format AMSBIB
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  • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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