Quantization Domains

TL;DR

This paper investigates the conditions under which classical field theories can be quantized to produce vacuum states with cyclic properties in bounded regions, drawing parallels to quantum field theory principles.

Contribution

It introduces elementary conditions ensuring bounded regions are quantization domains, linking classical field quantization to the Reeh-Schlieder property in quantum field theory.

Findings

Bounded regions can be quantization domains under certain conditions.

The work establishes a connection between classical and quantum field properties.

Provides a framework for understanding localization in classical field quantization.

Abstract

We study the quantization of certain classical field theories using reflection positivity. We give elementary conditions that ensure the resulting vacuum state is cyclic for products of quantum field operators, localized in a bounded Euclidean space-time region O at positive time. We call such a domain a quantization domain for the classical field. The fact that bounded regions are quantization domains in classical field theory is similar to the "Reeh-Schlieder" property in axiomatic quantum field theory.