Test Functions Space in Noncommutative Quantum Field Theory

Details Test Functions Space in Noncommutative Quantum Field Theory Test Functions Space in Noncommutative Quantum Field Theory

2007-06-12

arxiv.org/abs/0706.1712v3

JHEP 0809:125,2008

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, clarification of formula (1.6), typos fixed, minor language corrections

Scientific paper

10.1088/1126-6708/2008/09/125

It is proven that the $\star$-product of field operators implies that the space of test functions in the Wightman approach to noncommutative quantum field theory is one of the Gel'fand-Shilov spaces $S^{\beta}$ with $\beta < 1/2$. This class of test functions smears the noncommutative Wightman functions, which are in this case generalized distributions, sometimes called hyperfunctions. The existence and determination of the class of the test function spaces in NC QFT is important for any rigorous treatment in the Wightman approach.

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