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A new, more general derivation of the spin-statistics and PCT theorems is presented. It uses the notion of the analytic wave front set of (ultra)distributions and, in contrast to the usual approach, covers nonlocal quantum fields. The fields are defined as generalized functions with test functions of compact support in momentum space. The vacuum expectation… (More)

- M. A. Soloviev
- 2008

We formulate an equivalence relation between nonlocal quantum fields, generalizing the relative locality which was studied by Borchers in the framework of local QFT. The Borchers classes are shown to allow a natural extension involving nonlocal fields with arbitrarily singular ultraviolet behavior. Our consideration is based on the systematic employment of… (More)

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)

- M. A. Soloviev
- 1995

We prove that the distributions defined on the Gelfand-Shilov spaces S β α with β < 1, and hence more singular than hyperfunctions, retain the angular localiz-ability property. Specifically, they have uniquely determined support cones. This result enables one to develop a distribution-theoretic techniques suitable for the consistent treatment of quantum… (More)

- M. A. SOLOVIEV
- 2007

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)

- M. A. SOLOVIEV
- 2005

We elucidate the relation between the two ways of formulating causality in nonlocal quantum field theory: using analytic test functions belonging to the space S 0 (which is the Fourier transform of the Schwartz space D) and using test functions in the Gelfand-Shilov spaces S 0 α. We prove that every functional defined on S 0 has the same carrier cones as… (More)

The infinite series in Wick powers of a generalized free field are considered that are convergent under smearing with analytic test functions and realize a nonlocal extension of the Borchers equivalence classes. The nonlocal fields to which they converge are proved to be asymptotically commuting, which serves as a natural generalization of the relative… (More)

- M. A. Soloviev
- 1992

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)