Geodesic
Noncommutative deformations of quantum field theories, locality, and causality
Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 3, pp. 413-429

Voir la notice de l'article provenant de la source Math-Net.Ru

We investigate noncommutative deformations of quantum field theories for different star products, particularly emphasizing the locality properties and the regularity of the deformed fields. Using functional analysis methods, we describe the basic structural features of the vacuum expectation values of star-modified products of fields and field commutators. As an alternative to microcausality, we introduce a notion of $\theta$-locality, where $\theta$ is the noncommutativity parameter. We also analyze the conditions for the convergence and continuity of star products and define the function algebra that is most suitable for the Moyal and Wick–Voros products. This algebra corresponds to the concept of strict deformation quantization and is a useful tool for constructing quantum field theories on a noncommutative space–time.
Keywords: noncommutative quantum field theory, Moyal star product, Wick–Voros star product, locality, causality, topological algebra of entire functions. 
@article{TMF_2010_163_3_a6,
     author = {M. A. Soloviev},
     title = {Noncommutative deformations of quantum field theories, locality, and causality},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {413--429},
     publisher = {mathdoc},
     volume = {163},
     number = {3},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2010_163_3_a6/}
}
TY  - JOUR
AU  - M. A. Soloviev
TI  - Noncommutative deformations of quantum field theories, locality, and causality
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2010
SP  - 413
EP  - 429
VL  - 163
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2010_163_3_a6/
LA  - ru
ID  - TMF_2010_163_3_a6
ER  - 
%0 Journal Article
%A M. A. Soloviev
%T Noncommutative deformations of quantum field theories, locality, and causality
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2010
%P 413-429
%V 163
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2010_163_3_a6/
%G ru
%F TMF_2010_163_3_a6
M. A. Soloviev. Noncommutative deformations of quantum field theories, locality, and causality. Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 3, pp. 413-429. http://geodesic.mathdoc.fr/item/TMF_2010_163_3_a6/