Nonconformal Scalar Field in a Homogeneous Isotropic Space and the Method of Hamiltonian Diagonalization

TL;DR

This paper develops a method for diagonalizing the Hamiltonian of a nonconformal scalar field in homogeneous isotropic spaces, enabling finite particle creation rates and a consistent energy spectrum analysis.

Contribution

It introduces a modified energy-momentum tensor and a Hamiltonian diagonalization method for nonconformal scalar fields in curved spaces, ensuring finite particle densities.

Findings

Diagonalization of the Hamiltonian yields a finite particle density.

The modified energy-momentum tensor matches the conformal case for specific properties.

The Hamiltonian can be constructed canonically with a suitable variable choice.

Abstract

The diagonalization of the metrical Hamiltonian of a scalar field with an arbitrary coupling with a curvature in N-dimensional homogeneous isotropic space is performed. The energy spectrum of the corresponding quasiparticles is obtained. The energies of the quasiparticles corresponding to the diagonal form of the canonical Hamiltonian are calculated. The modified energy-momentum tensor with the following properties is constructed. It coincides with the metrical energy-momentum tensor for conformal scalar field. Under its diagonalization the energies of relevant particles of a nonconformal field coincide to the oscillator frequencies and the density of such particles created in a nonstationary metric is finite. It is shown that the Hamiltonian calculated with the modified energy-momentum tensor can be constructed as a canonical Hamiltonian under the special choice of variables.