The existing transformation from a relativistic real scalar field to a complex nonrelativistic 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 nonrelativistic action up to second order in small parameters. We also show that the transformation can be interpreted as a Bogoliubov transformation between relativistic and nonrelativistic creation and annihilation operators and comment on emerging symmetries in the nonrelativistic theory.

• Received 8 June 2020
• Accepted 27 July 2020

DOI:https://doi.org/10.1103/PhysRevD.102.036024

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Published by the American Physical Society