Abstract
We calculate the anomalous magnetic moment of the electron in the Chern–Simons theory in 2+1 dimensions with and without a Maxwell term, both at zero temperature as well as at finite temperature. In the case of the Maxwell–Chern–Simons (MCS) theory, we find that there is an infrared divergence, both at zero as well as at finite temperature, when the tree level Chern–Simons term vanishes, which suggests that a Chern–Simons term is essential in such theories. At high temperature, the thermal correction in the MCS theory behaves as 1βlnβM, where β denotes the inverse temperature and M, the Chern–Simons coefficient. On the other hand, we find no thermal correction to the anomalous magnetic moment in the pure Chern–Simons (CS) theory.
Highlights
Chern-Simons theories [1, 2] in 2 + 1 dimensions have been of interest from a variety of reasons and have led to many interesting phenomena in various branches of physics [3]
Conventionally one argues that the topological Chern-Simons term is an additional gauge invariant term that can be added to the action, the study of the anomalous magnetic moment, both at zero as well as finite temperature, reveals that such a term is, essential and in the absence of this term, physical quantities such as the magnetic moment cannot be defined because of infrared divergence
We have systematically studied the anomalous magnetic moment of the electron in the 2 + 1 dimensional Chern-Simons theory with or without a Maxwell term, both at zero and at finite temperature
Summary
Chern-Simons theories [1, 2] in 2 + 1 dimensions have been of interest from a variety of reasons and have led to many interesting phenomena in various branches of physics [3]. Conventionally one argues that the topological Chern-Simons term is an additional gauge invariant term that can be added to the action, the study of the anomalous magnetic moment, both at zero as well as finite temperature, reveals that such a term is, essential and in the absence of this term, physical quantities such as the magnetic moment cannot be defined because of infrared divergence. On the other hand shows that the Abelian theory can exhibit infrared divergence at zero temperature at one loop in physical quantities, such as the anomalous magnetic moment unless there is a tree level Chern-Simons mass.
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