Creation and annihilation operators in Schr\"odinger representation in curved backgrounds

TL;DR

This paper introduces a modified set of creation and annihilation operators in the Schrödinger representation that aligns with the Fock representation in curved backgrounds, considering non-unitary vacuums like Minkowski and Unruh.

Contribution

It proposes a new formulation of creation and annihilation operators compatible with the Fock representation in curved spacetime, extending previous approaches.

Findings

Compatible operators in Schrödinger and Fock representations

Relation between Minkowski and Unruh vacuums analyzed

Framework accommodates non-unitary vacuums in curved backgrounds

Abstract

I propose modified set of creation and annihilation operators for the Schr\"odinger representation which is compatible with the Fock representation which differs from previous works. I take into account the relation between different non-unitary vacuums obtained from restricted frameworks like the relation between the Minkowski and Unruh vacuums.