Real scalar field, non-relativistic limit, and cosmological expansion

Abstract

The existing transformation from a relativistic real scalar field to a complex non-relativistic scalar field by Namjoo, Guth, and Kaiser is generalized from Minkowski space to a more general background metric. In that case the transformation is not purely algebraic any more but determined by a differential equation. We apply the generalized transformation to a real scalar with ${\varphi }^4$ interaction on an Friedmann-Lemaître-Robertson-Walker cosmologically expanding background and calculate the resulting non-relativistic action up to second order in small parameters. We also show that the transformation can be interpreted as a Bogoliubov transformation between relativistic and non-relativistic creation and annihilation operators and comment on emerging symmetries in the non-relativistic theory.

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• Characterizing Klein-Fock-Gordon-Majorana particles in (1+1) dimensions
• Curved and expanding spacetime geometries in Bose-Einstein condensates
• Emergent quantum field theories on curved spacetimes in spinor Bose-Einstein condensates: from scalar to Proca fields