Abstract
In this paper, we discuss the noncommutative QED$_2$ in the S-matrix framework. We are interested in perturbatively proving that the exact Schwinger mass $\mu^2=\frac{e^2}{\pi}$ does not receive noncommutative corrections to any order in loop expansion. In this sense, the S-matrix approach is useful since it allows us to work with the effective action $\Gamma[A]$ (interaction term) to compute the corresponding gauge field 1PI two-point function at higher orders. Furthermore, by means of $\alpha^*$-cohomology, we generalize the QED$_2$ S-matrix analysis in the Moyal star product to all translation-invariant star products.
Highlights
Because of the lack of proper answers to some important questions in our description of nature, it is rather natural to look for alternative proposals in order to gain insights to improve our knowledge and fundamental theories
Low-dimensional field theory models are widely used in the description of many physical phenomena, whose applicability range from planar physics in condensed matter (2 þ 1) spacetime [1] to many fermions and integrable systems in (1 þ 1) spacetime [2]
Symmetry does not necessarily imply the existence of a massless gauge field, which is an example of dynamical mass generation, and that, due to the linear behavior of the electrostatic potential, fermions do not appear in the physical states and the spectrum of this theory includes a free massive boson
Summary
Because of the lack of proper answers to some important questions in our description of nature, it is rather natural to look for alternative proposals in order to gain insights to improve our knowledge and fundamental theories. Symmetry does not necessarily imply the existence of a massless gauge field, which is an example of dynamical mass generation, and that, due to the linear behavior of the electrostatic potential, fermions do not appear in the physical states and the spectrum of this theory includes a free massive boson This shows that the fermionic field is confined, which is in total analogy with the quark confinement phenomenon happening in quantum chromodynamics (QCD)—in this sense massless QED2 is considered as a toy model for QCD4. While in the present work, we propose the S-matrix approach for the photon one-loop effective action Γ1⁄2A to more conveniently concentrate on the analysis of the higher-loop noncommutative corrections to the physical pole of the photon propagator. V we summarize the results and present our final remarks
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