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We revisit the question of microcausality violations in quantum field theory on noncommutative spacetime, taking $O(x)=:phistarphi:(x)$ 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 at spacelike separation in the noncommuting directions. However, the matrix elements of this commutator exhibit a rapid falloff along an arbitrary spacelike direction irrespective of the type of noncommutativity. We also consider the star commutator for this observable and show that it fails to vanish even at spacelike separation in the commuting directions and completely violates causality. We conclude with a brief discussion about the modified Wightman functions which are vacuum expectation values of the star products of fields at different spacetime points.
Assigning an intrinsic constant dipole moment to any field, we present a new kind of associative star product, the dipole star product, which was first introduced in [hep-th/0008030]. We develop the mathematics necessary to study the corresponding no
The study of the heat-trace expansion in noncommutative field theory has shown the existence of Moyal nonlocal Seeley-DeWitt coefficients which are related to the UV/IR mixing and manifest, in some cases, the non-renormalizability of the theory. We s
We consider a noncommutative field theory with space-time $star$-commutators based on an angular noncommutativity, namely a solvable Lie algebra: the Euclidean in two dimension. The $star$-product can be derived from a twist operator and it is shown
The fuzzy disc is a discretization of the algebra of functions on the two dimensional disc using finite matrices which preserves the action of the rotation group. We define a $varphi^4$ scalar field theory on it and analyze numerically for three diff
It is by now well known that the Poincare group acts on the Moyal plane with a twisted coproduct. Poincare invariant classical field theories can be formulated for this twisted coproduct. In this paper we systematically study such a twisted Poincare