The Hamilton Operator and Quantum Vacuum for Nonconformal Scalar Fields in the Homogeneous and Isotropic Space

TL;DR

This paper analyzes the Hamiltonian and quantum vacuum states of nonconformal scalar fields in homogeneous isotropic spaces, deriving energy spectra and particle creation characteristics, with implications for quantum field theory in curved spacetime.

Contribution

It introduces a method to diagonalize Hamilton operators for nonconformal scalar fields and constructs a modified Hamiltonian that aligns with canonical form under specific variables.

Findings

Energy spectrum of quasiparticles derived

Finite particle density in nonstationary metrics

Modified Hamiltonian constructed as canonical operator

Abstract

The diagonalization of the metrical and canonical Hamilton operators of a scalar field with an arbitrary coupling, with a curvature in N-dimensional homogeneous isotropic space is considered in this paper. The energy spectrum of the corresponding quasiparticles is obtained and then the modified energy-momentum tensor is constructed; the latter coincides with the metrical energy-momentum tensor for conformal scalar field. Under the diagonalization of corresponding Hamilton operator the energies of relevant particles of a nonconformal field are equal to the oscillator frequencies, and the density of such particles created in a nonstationary metric is finite. It is shown that the modified Hamilton operator can be constructed as a canonical Hamilton operator under the special choice of variables.