caa a22 4500 467911584 CHVBK 20180406152850.0 cr unu---uuuuu 170328e20060501xx s 000 0 eng 10.1007/s11232-006-0068-7 doi (NATIONALLICENCE)springer-10.1007/s11232-006-0068-7 Soloviev M. Lebedev Physical Institute, RAS, Moscow, Russia aut Axiomatic formulations of nonlocal and noncommutative field theories [Elektronische Daten] [M. Soloviev] 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. Springer Science+Business Media, Inc., 2006 nonlocal quantum fields nationallicence causality nationallicence noncommutative field theory nationallicence Wightman functions nationallicence analytic functionals nationallicence Paley-Wiener-Schwartz theorem nationallicence Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 147/2(2006-05-01), 660-669 0040-5779 147:2<660 2006 147 11232 https://doi.org/10.1007/s11232-006-0068-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11232-006-0068-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Soloviev M. Lebedev Physical Institute, RAS, Moscow, Russia aut NATIONALLICENCE 773 0- Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 147/2(2006-05-01), 660-669 0040-5779 147:2<660 2006 147 11232 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer