Galilean electrodynamics: covariant formulation and Lagrangian

Mehra, Aditya; Sanghavi, Yaman

doi:10.1007/jhep09(2021)078

Cited by 7 publications

(9 citation statements)

References 30 publications

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“…For a theory with sources, one could take the same limits on the currents to write electric and magnetic equations of motion. To this effect, in [38] a composite albeit covariant Lagrangian was introduced, which consistently reproduces both electric and magnetic equations of motion.…”

Section: Covariant Lagrangian and Transformation Lawsmentioning

confidence: 99%

“…But they are electric inverse of the electric field strength and magentic inverse of the magentic field strength, in the same vein as defining the projective inverses for our Galilean tensors. To connect to the notation of [38], these are actually defined by the tilde conjugation, which acts via a Galilean contraction of gauge fields. For example, in the Electric case,…”

Section: Electric and Magnetic Invariantsmentioning

confidence: 99%

“…These manifolds in general have a fibre bundle structure that keeps temporal and spatial diffeomorphisms separate from each other. An attempt to write down a Galilean Covariant electrodynamics Lagrangian was recently made in [38], one which simultaneously describes electric and magnetic dominated realms of the theory. This Galilean Maxwell lagrangian will be the building block of our current work, and since that Lagrangian is manifestly invariant under the 4d GCA, we will try to introduce an explicit non-linear Covariant Lagrangian with a ModMaxlike form, consequently showing the GCA invariance for the same as well.…”

mentioning

confidence: 99%

“…In section 3 we will revisit Newton-Cartan structures and construction of a gauge field Lagrangian on such a structure. Here we will slightly differ from the approach of [38], and instead focus on the transformation of components of gauge fields under Galilean Conformal symmetries. We will also discuss in detail the structure of Galilean invariant field bilinears that will be important to our construction.…”

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confidence: 99%

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ModMax meets GCA

Banerjee¹,

Mehra²

2022

Preprint

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A maximally symmetric non-linear extension of Maxwell's theory in four dimensions called ModMax has been recently introduced in the literature. This theory preserves both electromagnetic duality and conformal invariance of the linear theory. In this short paper, we introduce a Galilean cousin of the ModMax theory, written in a covariant formalism, that is explicitly shown to be invariant under Galilean Conformal Symmetries. We discuss the construction of such a theory involving Galilean electromagnetic invariants, and show how the classical structure of the theory is invariant under the action of Galilean Conformal Algebra (GCA).

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Section: Covariant Lagrangian and Transformation Lawsmentioning

confidence: 99%

Section: Electric and Magnetic Invariantsmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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ModMax meets GCA

Banerjee¹,

Mehra²

2022

Preprint

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“…Initial works on Galilean gauge theories date back to the construction of Galilean electrodynamics by Le Ballac and Levy-Leblond [6] in the 1970s. The more recent papers in this direction are [7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Galilean Gauge Theories from Null Reductions

Bagchi,

Basu,

Islam

et al. 2022

Preprint

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The procedure of null reduction provides a concrete way of constructing field theories with Galilean invariance. We use this to examine Galilean gauge theories, viz. Galilean electrodynamics and Yang-Mills theories in spacetime dimensions 3 and 4. Different non-relativistic conformal symmetries arise in these contexts: Schrödinger symmetry in d = 3 and Galilean conformal symmetry in d = 4. A canonical analysis further reveals that the symmetries enhance to their infinite dimensional versions in phase space and pick up central extensions. In addition, for the Abelian theory, we discuss non-relativistic electromagnetic duality in d = 3 and its difference with the d = 4 version. We also mention some quantum aspects for both Abelian and non-Abelian theories.

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Galilean gauge theories from null reductions

Bagchi

Basu

Islam

et al. 2022

J. High Energ. Phys.

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The procedure of null reduction provides a concrete way of constructing field theories with Galilean invariance. We use this to examine Galilean gauge theories, viz. Galilean electrodynamics and Yang-Mills theories in spacetime dimensions 3 and 4. Different non-relativistic conformal symmetries arise in these contexts: Schrödinger symmetry in d = 3 and Galilean conformal symmetry in d = 4. A canonical analysis further reveals that the symmetries enhance to their infinite dimensional versions in phase space and pick up central extensions. In addition, for the Abelian theory, we discuss non-relativistic electro- magnetic duality in d = 3 and its difference with the d = 4 version. We also mention some quantum aspects for both Abelian and non-Abelian theories.

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Galilean electrodynamics: covariant formulation and Lagrangian

Cited by 7 publications

References 30 publications

ModMax meets GCA

ModMax meets GCA

Galilean Gauge Theories from Null Reductions

Galilean gauge theories from null reductions

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