A note on canonical quantization of fields on a manifold

TL;DR

This paper introduces a unified framework for quantizing linear canonical quantum fields on manifolds, enabling the construction of pure and mixed states and extending standard methods to new scenarios.

Contribution

It presents a generalized 'extended canonical quantization' method that broadens the scope of quantum field theory on manifolds beyond traditional approaches.

Findings

Unified treatment of pure and mixed states

Application to thermodynamical equilibrium states

Extension to quantum fields in curved spacetimes

Abstract

We propose a general construction of quantum states for linear canonical quantum fields on a manifold, which encompasses and generalizes the "standard" procedures existing in textbooks. Our method provides pure and mixed states on the same footing. A large class of examples finds a simple and unified treatment in our approach. Applications discussed here include thermodynamical equilibrium states for Minkowski fields and quantum field theory in the Rindler's and in the open de Sitter universes. Our approach puts the above examples into perspective and unravels new possibilities for quantization. We call our generalization "extended canonical quantization" as it is suited to attack cases not directly covered by the standard canonical approach.