Abstract
We investigate the existence of action for both the electric and magnetic sectors of Galilean Electrodynamics using Helmholtz conditions. We prove the existence of unique action in magnetic limit with the addition of a scalar field in the system. The check also implies the non existence of action in the electric sector of Galilean electrodynamics. Dirac constraint analysis of the theory reveals that there are no local degrees of freedom in the system. Further, the theory enjoys a reduced but an infinite dimensional subalgebra of Galilean conformal symmetry algebra as global symmetries. The full Galilean conformal algebra however is realized as canonical symmetries on the phase space. The corresponding algebra of Hamilton functions acquire a state dependent central charge.
Highlights
In higher dimensions the conformal symmetry groups are finite dimensional
We investigate the existence of action for both the electric and magnetic sectors of Galilean Electrodynamics using Helmholtz conditions
The question that naturally arises in such cases is that: given a set of equations of motion, is it possible to find a Lagrangian corresponding to them? In other words we would like to know whether a given set of second order partial differential equations governing the dynamics of a physical system can be obtained as Euler-Lagrange equations of some Lagrangian function
Summary
Galelian electrodynamics is the answer to the question whether there exists a consistent and physically meaningful non-relativistic theory of classical electromagnetism [10]. Instead of a single non relativistic limit, there are two different limits called electric and magnetic limits depending on the dominance of electric and magnetic effects respectively. Magnetic and electric limits are expressed in scaling of space-time coordinates and the difference in scaling of the gauge field components
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