Star product algebras of test functions
Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 1, pp. 3-17
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We prove that the Gelfand–Shilov spaces $S^{\beta}_{\alpha}$ are topological algebras
under the Moyal $\star$-product if and only if $\alpha\ge\beta$. These spaces
of test functions can be used to construct a noncommutative field theory.
The star product depends on the noncommutativity parameter continuously in their
topology. We also prove that the series expansion of the Moyal product
converges absolutely in $S^{\beta}_{\alpha}$ if and only if $\beta1/2$.
Keywords:
noncommutative quantum field theory, Moyal product, topological $*$-algebra, Gelfand–Shilov space.
@article{TMF_2007_153_1_a0,
author = {M. A. Soloviev},
title = {Star product algebras of test functions},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {3--17},
publisher = {mathdoc},
volume = {153},
number = {1},
year = {2007},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2007_153_1_a0/}
}
M. A. Soloviev. Star product algebras of test functions. Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 1, pp. 3-17. http://geodesic.mathdoc.fr/item/TMF_2007_153_1_a0/