Bogolyubov Quasiparticles in Constrained Systems

TL;DR

This paper develops a quantum field theory framework for the early universe in General Relativity, using Hamiltonian reduction and Bogoliubov quasiparticles to analyze particle creation during rapid cosmic expansion.

Contribution

It introduces a novel Hamiltonian reduction method and defines particles via measurable density, applying Bogoliubov transformations to describe early universe particle creation.

Findings

Successful formulation of quantum field theory in constrained cosmological systems

Identification of quasiparticles through diagonalization of equations of motion

Application to models with diverging Hubble parameter during early universe

Abstract

The paper is devoted to the formulation of quantum field theory for an early universe in General Relativity considered as the Dirac general constrained system. The main idea is the Hamiltonian reduction of the constrained system in terms of measurable quantities of the observational cosmology: the world proper time, cosmic scale factor, and the density of matter. We define " particles" as field variables in the holomorphic representation which diagonalize the measurable density. The Bogoliubov quasiparticles are determined by diagonalization of the equations of motion (but not only of the initial Hamiltonian) to get the set of integrals of motion (or conserved quantum numbers, in quantum theory). This approach is applied to describe particle creation in the models of the early universe where the Hubble parameter goes to infinity.