Boundary Poisson structure and quantization

TL;DR

This paper introduces a novel approach to boundary Poisson structures using causality and locality, demonstrating that canonical quantization is feasible for scalar fields with linear boundary conditions.

Contribution

It presents a new method for analyzing boundary Poisson structures and shows how to apply canonical quantization systematically in this context.

Findings

Boundary Poisson structures can be treated with causality and locality analysis.

Canonical quantization is applicable for scalar fields with linear boundary conditions.

The approach simplifies the quantization process for boundary-interacting fields.

Abstract

A new approach for treating boundary Poisson structures based on causality and locality analysis is proposed for a single scalar field with boundary interaction. For the case of linear boundary condition, it is shown that the usual canonical quantization can be applied systematically.