Abstract
In this paper, we construct a single Lagrangian for both limits of Galilean electrodynamics. The framework relies on a covariant formalism used in describing Galilean geometry. We write down the Galilean conformal algebra and its representation in this formalism. We also show that the Lagrangian is invariant under the Galilean conformal algebra in d = 4 and calculate the energy-momentum tensor.
Highlights
Classical electrodynamics is an example of a conformal field theory (CFT)
Invariance under finite-dimensional conformal transformations in the covariant formulation has been discussed in [1, 2]. This theory is anomalous at the quantum levels, but when we generalise to N = 4 Supersymmetric Yang-Mills (SYM), the conformal symmetries survive miraculously [3,4,5]
We first start with some features of the geometry of Galilean space-time which are pertinent to our formalism of Galilean conformal algebra (GCA) and Galilean electrodynamics
Summary
We will first discuss the geometry of Galilean spacetime and move to Galilean conformal algebra. We can have two kinds of metric tensors, represented by τμν and hμν respectively for contravariant and covariant vectors. In addition to these metric tensors, there are two more tensors defined in the literature These two will act like the metric tensors for the irreducible subspaces of the contravariant (up-indexed vectors) vector space and the covariant (down-indexed vectors) vector space under the action of Galilean boosts and rotations. It is easy to verify that these two vector spaces defined above are invariant and irreducible under the action of Galilean boosts and rotations. Where ci’s can be any real numbers and they will change under boosts and rotations
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