Field theory on noncommutative spacetimes: Quasiplanar Wick products

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.

On the problem of renormalizability in non‐commutative gauge field models – a critical review

“…However, this damping behaviour vanishes in the limit p µ → 0 ∀µ orp µ → 0 ∀µ, where the phase becomes unity. Naturally, in this limit the original divergence has to reappear, and in the case of a quadratic divergence is represented in the form 1 There have been claims, that the UV/IR mixing is not present in a Minkowskian non-commutative QFT if one considers proper Feynman rules taking into account a generalized notion of time ordering [14,15,16,17,18,19]. However, these conjectures still lack a rigorous proof.…”

Schwinger Functions in Noncommutative Quantum Field Theory

“…Observe also that compared to the ordinary twisting in (3.1), the factor 2 in the oscillating factor appears, since in the calculations, two oscillating factors as in (3.1) either cancel or (in the above case) add up, see [1,2]. In fact, if we consider the three different contributions to the 4-point function as explained after equation (3.2), we find that two of them are the same as in the commutative case (the twistings cancel), and only in the contribution where the first field is contracted with the third, and the second with the fourth, the twistings add up (hence the factor 2).…”

“…In [1,2], it was shown how 2n-point functions are calculated in hyperbolic massive scalar field theory on the noncommutative Moyal space (n-point functions for n odd still vanish). Their general properties were investigated in [2].…”

Magnetic Backgrounds and Noncommutative Field Theory

“…Thus the D-brane worldvolume becomes a noncommutative space. Because of the point particle limit ℓ s → 0 taken in (45), the effective dynamics is governed in this limit as usual by a field theory for the massless open string modes. Following the analysis of the previous Section, we thus find that the low-energy effective field theories on D-branes get modified now to those defined with noncommuting coordinates, or equivalently by star-products of the fields.…”