Abstract
We present a generalization of the so-called Maxwellian extended Bargmann algebra by considering a non-relativistic limit to a generalized Maxwell algebra defined in three spacetime dimensions. The non-relativistic Chern-Simons gravity theory based on this new algebra is also constructed and discussed. We point out that the extended Bargmann and its Maxwellian generalization are particular sub-cases of the generalized Maxwellian extended Bargmann gravity introduced here. The extension of our results using the semigroup expansion method is also discussed.
Highlights
It is natural to address the question whether such generalized Maxwell algebra admits a welldefined NR version in three spacetime dimensions
We will show that there is a relation between the number of U (1) generators required in the relativistic theory and the number of elements of the semigroup involved in the semigroup expansion method
In this paper we have presented a generalization of the Maxwellian extended Bargmann gravity introduced in [44]
Summary
We briefly review the generalized Maxwell algebra and present the construction of a three-dimensional CS gravity action invariant under such algebra. In order to construct the relativistic CS gravity action invariant under the algebra (2.1) we shall consider the most general non-vanishing components of the invariant tensor [55]. Gauge fields in order to avoid infinities and cancel divergences Such enlargement will allow to define a proper NR limit whose NR algebra will admit non-degenerate bilinear form. Let us consider a particular U (1) enlargement of the generalized Maxwell algebra by adding four extra U (1) one-form gauge fields to the field content as. The new relativistic algebra, [generalized Maxwell]⊕u (1) algebra, admits the non-vanishing components of the invariant tensor (2.6) along with. Considering the gauge connection one-form (2.10) and the invariant tensor given by (2.6) and (2.11) in the general expression of the CS action (2.2), we find the following relativistic CS gravity action. We will show that there is a relation between the number of U (1) generators required in the relativistic theory and the number of elements of the semigroup involved in the semigroup expansion method
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