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Teoreticheskaya i Matematicheskaya Fizika, 2007, Volume 153, Number 1, Pages 3–17
DOI: https://doi.org/10.4213/tmf6117
(Mi tmf6117)
 

This article is cited in 23 scientific papers (total in 23 papers)

Star product algebras of test functions

M. A. Soloviev

P. N. Lebedev Physical Institute, Russian Academy of Sciences
References:
Abstract: 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 $\beta<1/2$.
Keywords: noncommutative quantum field theory, Moyal product, topological $*$-algebra, Gelfand–Shilov space.
Received: 12.12.2006
English version:
Theoretical and Mathematical Physics, 2007, Volume 153, Issue 1, Pages 1351–1363
DOI: https://doi.org/10.1007/s11232-007-0119-8
Bibliographic databases:
Language: Russian
Citation: M. A. Soloviev, “Star product algebras of test functions”, TMF, 153:1 (2007), 3–17; Theoret. and Math. Phys., 153:1 (2007), 1351–1363
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf6117
  • https://doi.org/10.4213/tmf6117
  • https://www.mathnet.ru/eng/tmf/v153/i1/p3
  • This publication is cited in the following 23 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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