Effective Hamiltonian for non-minimally coupled scalar fields

TL;DR

This paper derives an effective Hamiltonian for non-minimally coupled scalar fields in curved spacetime, incorporating gravity coupling and scalar self-interaction, extending the Klein-Gordon equation to relativistic regimes.

Contribution

It introduces a relativistic effective Hamiltonian that generalizes the Klein-Gordon equation to include non-minimal gravitational coupling and scalar field self-interactions.

Findings

Derived an effective Hamiltonian for non-minimally coupled scalar fields.

Extended Klein-Gordon equation to curved spacetime with additional interactions.

Provides a foundation for further studies in quantum field theory in curved spacetime.

Abstract

Performing a relativistic approximation as the generalization to a curved spacetime of the flat space Klein-Gordon equation, an effective Hamiltonian which includes non-minimial coupling between gravity and scalar field and also quartic self-interaction of scalar field term is obtained.