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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.
We consider the non-relativistic limit of gravity in four dimensions in the first order formalism. First, we revisit the case of the Einstein-Hilbert action and formally discuss some geometrical configurations in vacuum and in the presence of matter
We obtain a new form for the action of a nonrelativistic particle coupled to Newtonian gravity. The result is different from that existing in the literature which, as shown here, is riddled with problems and inconsistencies. The present derivation is
We present a new approach to the problem of the thermodynamical equilibrium of a quantum relativistic fluid in a curved spacetime in the limit of small curvature. We calculate the mean value of local operators by expanding the four-temperature Killin
We analyze a few illustrative examples of scenarios in which relativistic symmetries are deformed by Planck-scale effects in particle-type-dependent manner. The novel mathematical structures required by such scenarios are the mixing coproducts, which
We build the general conformally invariant linear wave operator for a free, symmetric, second-rank tensor field in a d-dimensional ($dgeqslant 2$) metric manifold, and explicit the special case of maximally symmetric spaces. Under the assumptions mad