Abstract
The photon self-energy of the noncommutative Schwinger model at two- and three-loop order is analyzed. It is shown that the mass spectrum of the model does not receive any correction from the noncommutativity parameter (theta ) at these orders. Also it remains unchanged to all orders. The exact one-loop effective action for the photon is also calculated.
Highlights
The idea of noncommutative quantum field theory originates from the 1940s, when it was applied to cure the divergencies in quantum field theory before the renormalization approach was born [1]
It can be shown that the other graphs, Page 5 of 10 2921 which appeared at three-loop level, have a fermionicloop momentum-independent noncommutative phase factor
We have concentrated on the mass spectrum of the noncommutative Schwinger model with Euclidean signature at higher loops
Summary
The idea of noncommutative quantum field theory originates from the 1940s, when it was applied to cure the divergencies in quantum field theory before the renormalization approach was born [1]. It was demonstrated that the divergencies were not removed [2] Later on, it was shown in [3] that the noncommutative quantum field theory describes effectively the low energy limit of the string theory on a noncommutative manifold. The purpose of this paper is to concentrate on the mass spectrum of the theory at higher loops. The commutative counterpart of this model, the Schwinger model, was studied in [10] where it was shown that the photon in two dimensions acquires dynamical mass, arising from the loop effect, without gauge symmetry breaking. 3, to obtain the mass spectrum of the theory at two- and three-loop order, the photon self-energy is studied. 5, we demonstrate that the noncommutative one-loop effective action for the photon is exactly the same as the commutative counterpart.
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