Field Theory on Noncommutative Spacetimes: Quasiplanar Wick Products
D. Bahns, S. Doplicher, K. Fredenhagen, G. Piacitelli
TL;DR
This paper introduces quasiplanar Wick products for quantum field theories on noncommutative spacetime, providing a new way to define local counterterms and analyze perturbative expansions.
Contribution
It defines quasiplanar Wick products and admissible counterterms, extending Wick's theorem to noncommutative quantum field theories with a focus on locality.
Findings
Defined admissible counterterms for noncommutative QFTs
Constructed quasiplanar Wick products by subtracting specific counterterms
Derived an analogue of Wick's theorem for noncommutative spacetime
Abstract
We give a definition of admissible counterterms appropriate for massive quantum field theories on the noncommutative Minkowski space, based on a suitable notion of locality. We then define products of fields of arbitrary order, the so-called quasiplanar Wick products, by subtracting only such admissible counterterms. We derive the analogue of Wick's theorem and comment on the consequences of using quasiplanar Wick products in the perturbative expansion.
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