Demystification of Non-relativistic Theories in Curved Background

Abstract

We discuss a new formalism for constructing a non-relativistic (NR) theory in curved background. Named as galilean gauge theory, it is based on gauging the global galilean symmetry. It provides a systematic algorithm for obtaining the covariant curved space time generalisation of any NR theory defined in flat space time. The resulting background is just the Newton- Cartan manifold. The example of NR free particle is explicitly demonstrated.

5 pages, Essay written for the Gravity Research Foundation 2020 Awards for Essays on Gravitation (Honorable mention) To appear in IJMPD (special issue)

References in corpus (3)

• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Newtonian Gravity and the Bargmann Algebra
• A new formulation of non-relativistic diffeomorphism invariance

Cited by in corpus (1)

• Covariant Formulation of the Newton-Hooke Particle and its Canonical Analysis