Hamiltonian Formulation of Higher Rank Symmetric Gauge Theories

TL;DR

This paper provides a Hamiltonian analysis of higher rank symmetric gauge theories, revealing their connection to noncommutative geometry, fluid dynamics, and magnetohydrodynamics, with a focus on the traceless scalar charge theory.

Contribution

It introduces a Hamiltonian formulation for higher rank symmetric gauge theories, including a new action form and analysis of their global symmetries and algebraic structures.

Findings

Deduced a new Hamiltonian form for higher rank gauge theories.

Identified a noncommuting charge algebra related to Landau level physics.

Connected gauge theory symmetries to noncommutative fluid dynamics.

Abstract

Recent discussions of higher rank symmetric (fractonic) gauge theories have revealed the important role of Gauss constraints. This has prompted the present study where a detailed hamiltonian analysis of such theories is presented. Besides a general treatment, the traceless scalar charge theory is considered in details. A new form for the action is given which, in 2+1 dimensions, yields area preserving diffeomorphisms. Investigation of global symmetries reveals that this diffeomorphism invariance induces a noncommuting charge algebra that gets exactly mapped to the algebra of coordinates in the lowest Landau level problem. Connections of this charge algebra to noncommutative fluid dynamics and magnetohydrodynamics are shown.