Star product algebras of test functions

Details Star product algebras of test functions Star product algebras of test functions

2007-08-06

arxiv.org/abs/0708.0811v2

Theor.Math.Phys.153:1351-1363,2007; Teor.Mat.Fiz.153:3-17,2007

Physics

Mathematical Physics

AMS-LaTeX, 12 pages, no figures; typos corrected, minor changes to agree with published version

Scientific paper

10.1007/s11232-007-0119-8

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 in quantum field theory on noncommutative spacetime. 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 $\beta<1/2$.

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