Quantization of Scalar Fields in Curved Background and Quantum Algebras

TL;DR

This paper demonstrates how deforming the algebra of scalar field operators in Minkowski space can lead to their canonical quantization in curved spacetime, linking the deformation parameter to gravity and recovering thermal properties.

Contribution

It introduces a novel algebraic deformation approach that connects Minkowski and curved spacetime quantizations of scalar fields, clarifying the role of the deformation parameter as related to gravity.

Findings

Deformation parameter q is related to the gravitational field.

Thermal properties are recovered in the deformed algebra formalism.

Application to Schwarzschild and Rindler spacetimes confirms the approach.

Abstract

We show that a suitable deformation of the algebra $h_k(1)$ of the creation and annihilation operators for a complex scalar field, initially quantized in Minkowski space--time, induces the canonical quantization of the same field in a generic gravitational background. This discloses the physical meaning of the deformation parameter $q$ which turns out to be related to the gravitational field. The thermal properties are re-obtained in this formalism, and the application to Schwarzschild and Rindler space-times are carried out.