Maslov’s complex germ and the Weyl–Moyal algebra in quantum mechanics and in quantum field theory, math-ph/0702094

Abstract

Abstract. The paper is a survey of some author’s results related with the Maslov–Shvedov method of complex germ and with quantum field theory. The main idea is that many results of the method of complex germ and of perturbative quantum field theory can be made more simple and natural if instead of the algebra of (pseudo)differential operators one uses the Weyl algebra (operators with Weyl symbols) with the Moyal ∗-product

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