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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 7: Classical Field Theory
MP 7.2: Vortrag
Dienstag, 31. März 2020, 18:05–18:25, H-HS VII
Real scalar field, non-relativistic limit, and expansion — •Lars Heyen and Stefan Flörchinger — Institut für Theoretische Physik Heidelberg, Heidelberg, Germany
We generalise the existing transformation from a relativistic real scalar to a complex scalar with a Schroedinger-like equation of motion by Namjoo, Guth and Kaiser from a Minkowskian to a more general background metric. Then we apply the transformation to a real scalar on a FLRW background and calculate the effective non-relativistic potential up to second order in small parameters for a φ4 interaction in the relativistic theory. The non-trivial background introduces a term proportional to Im(ψ* ∇2 ψ) in the effective potential. Further, we show that the transformation can also be interpreted as a Bogoliubov transformation between relativistic and non-relativistic creation and annihilation operators.