Bose-Einstein condensation as symmetry breaking in curved spacetime and in spacetimes with boundaries.

Abstract

A quantum field theory treatment of Bose-Einstein condensation for a charged, noninteracting scalar field in a static spacetime with a possible spatial boundary is given. An interpretation is presented in terms of symmetry breaking to give a nonconstant scalar field expectation value. The method used is a computation of the effective action in the high-temperature limit. Results are obtained for static spacetimes of general dimension. The critical temperature for Bose-Einstein condensation is obtained in terms of the lowest eigenvalue of the Laplacian with the scalar field subject to the appropriate boundary conditions. A number of applications are provided for flat spacetimes with and without boundaries, and to curved spacetimes. In special cases where the scalar field expectation value is constant, some previously known results are obtained; in other cases, new results are found.