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High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
Abstract:
We construct the free Lagrangian of the magnetic sector of Carrollian
electrodynamics, which surprisingly, is not obtainable as an ultra-relativistic
limit of Maxwellian Electrodynamics. The construction relies on Helmholtz
integrability condition for differential equations in a self consistent
algorithm working hand in hand with imposing invariance under infinite
dimensional Conformal Carroll algebra (CCA). It requires inclusion of new
fields in the dynamics and the system in free of gauge redundancies. We
calculate two-point functions in the free theory based entirely on symmetry
principles. We next add interaction (quartic) terms to the free Lagrangian,
strictly constrained by conformal invariance and Carrollian symmetry. Finally,
a successful dynamical realization of infinite dimensional CCA is presented at
the level of charges, for the interacting theory. In conclusion, we calculate
the Poisson brackets for these charges.
