Renormalization of Galilean electrodynamics

Shira Chapman,Lorenzo Di Pietro,Kevin T Grosvenor,Ziqi Yan

doi:10.1007/jhep10(2020)195

Abstract

We study the quantum properties of a Galilean-invariant abelian gauge theory coupled to a Schrödinger scalar in 2+1 dimensions. At the classical level, the theory with minimal coupling is obtained from a null-reduction of relativistic Maxwell theory coupled to a complex scalar field in 3+1 dimensions and is closely related to the Galilean electromagnetism of Le-Bellac and Lévy-Leblond. Due to the presence of a dimensionless, gauge-invariant scalar field in the Galilean multiplet of the gauge-field, we find that at the quantum level an infinite number of couplings is generated. We explain how to handle the quantum corrections systematically using the background field method. Due to a non-renormalization theorem, the beta function of the gauge coupling is found to vanish to all orders in perturbation theory, leading to a continuous family of fixed points where the non-relativistic conformal symmetry is preserved.

Highlights

System is expected to gain a scaling symmetry, which can treat space and time differently in the absence of a boost symmetry
We study the quantum properties of a Galilean-invariant abelian gauge theory coupled to a Schrodinger scalar in 2+1 dimensions
We demonstrate that the stress tensor and mass current associated with the theory (2.23) obey the identities (2.3)–(2.6) and scalar Galilean electrodynamics (sGED) is Schrodinger invariant at the classical level for any value of the couplings J [M ], V[M ] and E[M ]

Summary

Introduction

System is expected to gain a scaling symmetry, which can treat space and time differently in the absence of a boost symmetry. In 2+1 dimensions, an action for gauge fields with the right symmetry is the Chern-Simons (CS) term Another notable example of Schrodinger-invariant quantum field theory, which describes anyons, is obtained by coupling a CS gauge field to a Schrodinger scalar [6, 15,16,17,18,19,20]. A different type of Schrodinger-invariant gauge theory, that can be defined in any number of space dimensions, has been proposed in the literature [21,22,23] This theory can be obtained from two different non-relativistic limits of Maxwell’s equations, known as the electric and magnetic limits [21], combined in a Galilean-invariant Lagrangian using auxiliary fields [22].1.

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Methods

Conclusion