Abstract
In this work, we show that Lorentz invariant theories in 1+1 dimensions admit new terms inspired by Very Special Relativity (VSR) theories. We have studied the Schwinger model in VSR. We show the axial current is classically conserved in the presence of a mass term coming from the VSR invariant terms but without standard Lorentz invariant mass. Furthermore, it is shown that both the vector current as well as the axial current are modified with respect to the free case when the fermion is coupled to an external electromagnetic field due to the nonlocal operator present in the theory. The axial anomaly is computed, and we found the same standard topological invariant with a modification in the coefficient.
Highlights
Quantum Electrodynamics in 1 + 1 dimensions (QED2) has been studied, and it has an exact solution discovered by Schwinger[1] when the fermion remains massless
Despite the massive Schwinger model is not exactly solvable, it has been reviewed too[10, 11]. Another essential feature in the Schwinger model is the presence of the chiral anomaly, which is easier to compute than in four dimensions
We will consider from here M = 0 to study the Schwinger model in Very Special Relativity (VSR)
Summary
Quantum Electrodynamics in 1 + 1 dimensions (QED2) has been studied, and it has an exact solution discovered by Schwinger[1] when the fermion remains massless. We can add to the lagrangian terms with fractions which contain n as in the numerator as in the denominator, because they are invariant under the Lorentz transformation This kind of terms have been studied in four dimensional VSR theories (see for instance [15,16,17,18]), where the null vector (1, 0, 0, 1) transforms in the same way under SIM (2) group transformations. These terms have not been incorporated in two dimensional works in Lorentz invariant theories and they could be added
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