2008/09/25 by Gaetano Fiore · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Commutative property #Geometry #Mathematical physics #Mathematics #Minkowski space #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Observable #Physics #Pure mathematics #Quantum field theory #Quantum mechanics #Scalar (mathematics) #Star product #Theoretical physics #hep-th
paper · pdf · doi:10.1142/9789812833556_0005
Latex file, 21 pages
arxiv created 2008/09/25 · openalex publication_date 2008/10/01 · openalex created_date 2016/06/24 · arxiv updated 2017/08/23 · openalex updated_date 2026/08/05
We explore some general consequences of a consistent formulation of relativistic quantum field theory (QFT) on the Groenewold-Moyal-Weyl noncommutative versions of Minkowski space with covariance under the twisted Poincare' group of Chaichian et al. [12], Wess [44], Koch et al. [31], Oeckl [34]. We argue that a proper enforcement of the latter requires braided commutation relations between any pair of coordinates x, y generating two different copies of the space, or equivalently a ⋆-tensor product f(x)⋆ g(y) (in the parlance of Aschieri et al. [3]) between any two functions depending on x,y. Then all differences (x-y)μ behave like their undeformed counterparts. Imposing (minimally adapted) Wightman axioms one finds that the n-point functions fulfill the same general properties as on commutative space. Actually, upon computation one finds (at least for scalar fields) that the n-point functions remain unchanged as functions of the coordinates' differences both if fields are free and if they interact (we treat interactions via time-ordered perturbation theory). The main, surprising outcome seems a QFT physically equivalent to the undeformed counterpart (to confirm it or not one should however first clarify the relation between n-point functions and observables, in particular S-matrix elements). These results are mainly based on a joint work [24] with J. Wess