Mikhail A. Soloviev

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We analyze functional analytic aspects of axiomatic formulations of nonlocal and noncommutative quantum field theories. In particular, we completely clarify the relation between the asymptotic commutativity condition, which ensures the CPT symmetry and the standard spin-statistics relation for nonlocal fields, and the regularity properties of the retarded(More)
We prove that the Gelfand-Shilov spaces S β α are topological algebras under the Moyal star product if and only if α ≥ β. These spaces of test functions can be used in quantum field theory on noncommutative spacetime. The star product depends continuously in their topology on the noncommutativity parameter. We also prove that the series expansion of the(More)
We revisit the question of microcausality violations in quantum field theory on noncommutative spacetime, taking O(x) =: φ ⋆ φ : (x) as a sample observable. Using methods of the theory of distributions, we precisely describe the support properties of the commutator [O(x), O(y)] and prove that, in the case of space-space noncommutativity, it does not vanish(More)
The mathematical formalism commonly used in treating nonlocal highly singular interactions is revised. The notion of support cone is introduced which replaces that of support for nonlocalizable distributions. Such support cones are proven to exist for distributions defined on the Gelfand-Shilov spaces S β , where 0 < β < 1. This result leads to a refinement(More)
In this paper, we introduce the condition of θ-locality which can be used as a substitute for microcausality in quantum field theory on noncommutative spacetime. This condition is closely related to the asymptotic commutativity which was previously used in nonlocal QFT. Heuristically, it means that the commutators of observables behave at large spacelike(More)