Perturbative Analysis of the Seiberg–witten Map

Abstract

We investigate the quantization of the θ-expanded noncommutative U(1) Yang-Mills action, obtained via the Seiberg-Witten map. As expected we find non-renormalizable terms. The one-loop propagator corrections are gauge independent, and lead us to a unique extention of the noncommutative classical action. We interpret our results as a requirement that also the trace in noncommutative field theory should be deformed.

Schwinger model in noncommutating space–time

“…and the equations of motion for φ and π φ arė φ = (1 + eθφ) π φ (29) π φ = φ ′′ − e 2 φ − eθ 2 π 2 φ + φ ′2 + 2φφ ′′ + 3e 2 φ 2…”

“…We analyzed the model in the commutative equivalent representation [31,32,33,34,27] using a perturbative Seiberg-Witten map [28,29,30]. Following [8] we have assumed the applicability of a usual Hamiltonian analysis of the commutative equivalent model.…”

Some remarks on Feynman rules for non-commutative gauge theories based on groupsG$\not=$U(N)

“…The Seiberg-Witten map for the ghost C looks like that for the gauge transformation in (4) while the antighost is kept unchanged [11], i.e.…”

“…Therefore, looking at the n-point functions of the, in terms of a, c,c, composite operators A, C,C (see (4), (6)) the summation of the perturbation theory with respect to s 1 [a, c,c] − i log J must yield the free field result guaranteed by (11). 5 On the other side for G ⊂ U(N) we cannot directly evaluate (11) and are forced to work with (12). It will turn out to be useful to study both U(N) and G ⊂ U(N) in parallel.…”

Remarks on nonlinear electrodynamics

“…The main reason for this is that the SM does not include a quantum theory of gravitation, as well as the need to understand and to overcome theoretical difficulties in quantum gravity research. An attempt along this direction has been to consider quantum field theories allowing noncommuting position operators [28][29][30][31][32][33], where this noncommutativity is an intrinsic property of space-time. These studies were first made by using a star product (Moyal product).…”