General boundary quantum field theory: Foundations and probability interpretation

TL;DR

This paper develops a general boundary quantum field theory framework that extends standard quantum mechanics to arbitrary spacetime regions and hypersurfaces, providing a foundational basis and probability interpretation.

Contribution

It introduces a comprehensive foundational formulation of boundary quantum field theory, generalizing quantum mechanics to arbitrary spacetime regions and hypersurfaces with core axioms and probability interpretation.

Findings

Standard quantum mechanics is recovered as a special case.

The framework incorporates spacetime symmetries and unitarity.

It provides a basis for formulating quantum field theories in arbitrary regions.

Abstract

We elaborate on the proposed general boundary formulation as an extension of standard quantum mechanics to arbitrary (or no) backgrounds. Temporal transition amplitudes are generalized to amplitudes for arbitrary spacetime regions. State spaces are associated to general (not necessarily spacelike) hypersurfaces. We give a detailed foundational exposition of this approach, including its probability interpretation and a list of core axioms. We explain how standard quantum mechanics arises as a special case. We include a discussion of probability conservation and unitarity, showing how these concepts are generalized in the present framework. We formulate vacuum axioms and incorporate spacetime symmetries into the framework. We show how the Schroedinger-Feynman approach is a suitable starting point for casting quantum field theories into the general boundary form. We discuss the role of operators.