On the question of symmetries in non-relativistic diffeomorphism invariant theories

Understand

A novel algorithm is provided to couple a Galilean invariant model with curved spatial background by taking nonrelativistic limit of a unique minimally coupled relativistic theory, which ensures Galilean symmetry in the flat limit and canonical transformation of the original fields.

• That the twin requirements are fulfilled is ensured by a new field, the existence of which was demonstrated recently from Galilean gauge theory.
• The ambiguities and anomalies concerning the recovery of Galilean symmetry in the flat limit of spatial non relativistic diffeomorphic theories, reported in the literature, are focused and resolved from a new angle.