# Non Local Global Symmetries of a Free Scalar Field in a Bounded Domain

## TL;DR

This paper explores non-local global symmetries of a free scalar field in a bounded domain, extending the understanding of BMS symmetries beyond asymptotic regions by considering non-local generators in phase space.

## Contribution

It introduces a general framework for identifying all possible global symmetries of free fields, including non-local ones, in a bounded Minkowski spacetime with boundary conditions.

## Key findings

- Complete set of global symmetries identified for the 2+1D scalar field
- Most symmetries are dynamical, some relate to conserved quantities
- Boundary conditions influence the symmetry structure

## Abstract

BMS symmetries have been attracting a great deal of interest in recent years. Originally discovered as being the symmetries of asymptotically flat spacetime geometries at null infinity in General Relativity, BMS symmetries have also been shown to exist for free field theories over Minkowski spacetime. In wanting to better understand their status and the underlying reasons for their existence, this work proposes a general rationale towards identifying all possible global symmetries of a free field theory over Minkowski spacetime, by allowing the corresponding conserved generators not to be necessarily spatially local in phase space since fields and their conjugate momenta are intrinsically spatially non local physical entities. As a preliminary towards a separate study of the role of asymptotic states for BMS symmetries in an unbounded Minkowski spacetime, the present discussion focuses first onto a 2+1 dimensional free scalar field theory in a bounded spatial domain with the topology of a disk and an arbitrary radial Robin boundary condition. The complete set of global symmetries of that system, most of which are dynamical symmetries but include as well those generated by the local total energy and angular-momentum of the field, is thereby identified.