Effective Lagrangian for self-interacting scalar field theories in curved spacetime

TL;DR

This paper derives the one-loop effective Lagrangian for a self-interacting scalar field in curved spacetime, analyzing how curvature influences phase transitions using advanced regularization and heat-kernel methods.

Contribution

It introduces a method to compute the effective Lagrangian up to second order in background variations and quadratic in curvature, advancing understanding of scalar fields in curved spacetime.

Findings

Curvature affects phase transition behavior.

Effective Lagrangian derived up to second order in background variations.

Method applicable to various physically relevant spacetimes.

Abstract

We consider a self-interacting scalar field theory in a slowly varying gravitational background field. Using zeta-function regularization and heat-kernel techniques, we derive the one-loop effective Lagrangian up to second order in the variation of the background field and up to quadratic terms in the curvature tensors. Specializing to different spacetimes of physical interest, the influence of the curvature on the phase transition is considered.