Noncommutative Deformations of Wightman Quantum Field Theories
نویسنده
چکیده
Quantum field theories on noncommutative Minkowski space are studied in a model-independent setting by treating the noncommutativity as a deformation of quantum field theories on commut ative space. Starting from an arbitrary Wightman theory, we consider special vacuum representations of its Weyl-Wigner deformed counterpart. In such representations, the effect of the noncommutativity on the basic structures of Wightman theory, in particular the covariance, locality and regularity properties of the fields, the structure of the Wightman functions, and the commutative limit, is analyzed. Despite the nonlocal structure introduced by the noncommutativity, the deformed quantum fields can still be localized in certain wedge-shaped regions, and may therefore be used to compute noncommutative corrections to two-particle S-matrix elements.
منابع مشابه
Test Functions Space in Noncommutative Quantum Field Theory
Abstract: It is proven that the ⋆-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 with β < 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 de...
متن کاملNon-Commutative Quantum Field Theories in Terms of Tempered Ultrahyperfunctions
In the present paper, we wish to consider the quantum field theory on non-commutative spacetimes in terms of the tempered ultrahyperfunctions of Sebastião e Silva corresponding to a convex cone, within the framework formulated by Wightman. Tempered ultrahyperfunctions are representable by means of holomorphic functions. As is well known there are certain advantages to be gained from the represe...
متن کاملQuantum Fields on Noncommutative Spacetimes: Theory and Phenomenology
In the present work we review the twisted field construction of quantum field theory on noncommutative spacetimes based on twisted Poincaré invariance. We present the latest development in the field, in particular the notion of equivalence of such quantum field theories on a noncommutative spacetime, in this regard we work out explicitly the inequivalence between twisted quantum field theories ...
متن کاملOn a noncommutative deformation of the Connes-Kreimer algebra
We study a noncommutative deformation of the commutative Hopf algebra HR of rooted trees which was shown by Connes and Kreimer to describe the mathematical structure of renormalization in quantum field theories. The requirement of the existence of an antipode for the noncommutative deformation leads to a natural extension of the algebra. Noncommutative deformations of HR might be relevant for r...
متن کاملAxiomatic formulations of nonlocal and noncommutative field theories
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 Green’s functions in momentum space tha...
متن کامل