Holomorphic Quantization of Linear Field Theory in the General Boundary Formulation

TL;DR

This paper develops a rigorous holomorphic quantization scheme for linear field theories within the general boundary formulation, establishing a geometric quantization approach that produces consistent quantum field theories with well-defined states and amplitudes.

Contribution

It introduces a novel holomorphic quantization method for linear fields in the general boundary framework, including vacuum and coherent states, and applies it to Klein-Gordon evanescent waves.

Findings

Validated TQFT axioms in this framework

Constructed state spaces as holomorphic functions

Quantized evanescent Klein-Gordon waves

Abstract

We present a rigorous quantization scheme that yields a quantum field theory in general boundary form starting from a linear field theory. Following a geometric quantization approach in the K\"ahler case, state spaces arise as spaces of holomorphic functions on linear spaces of classical solutions in neighborhoods of hypersurfaces. Amplitudes arise as integrals of such functions over spaces of classical solutions in regions of spacetime. We prove the validity of the TQFT-type axioms of the general boundary formulation under reasonable assumptions. We also develop the notions of vacuum and coherent states in this framework. As a first application we quantize evanescent waves in Klein-Gordon theory.