Physics

Arpita Mitra
S. N. Bose National Centre for Basic Sciences, Kolkata

Absract: 

Motivated by recent applications of non-relativistic field theories on curved spacetimes, we investigate the minimal coupling of massive matter fields to curved non-relativistic backgrounds. Unlike relativistic curved backgrounds, general covariance in the nonrelativistic context requires careful consideration due to the absolute nature of Newtonian time. We have derived the coupling of fields by localizing the global spacetime symmetries of the matter action on the Euclidean background. The new fields introduced during the localization of the Galilean symmetry can be identified with the tetrads and spin connection of the Newton-Cartan spacetime. Further including the anisotropic scale transformation in the localization procedure, the background we derive is the scale invariant extension of the Newton-Cartan gravity, which we have called the Weyl-rescaled Newton-Cartan background. Unlike the relativistic case these backgrounds possess two degenerate metrics as a direct consequence of the unequal footing of time and space. It will be of interest to study how these two metrics affect the dynamics of fields coupled to them. As a specific example, we consider the case of an incompressible ideal fluid in its rest frame and derive the thermodynamic and hydrodynamic relations satisfied on these backgrounds. Key differences with the relativistic formulation are highlighted and discussed.