Advances in Theoretical and Mathematical Physics

General boundary quantum field theory: Foundations and probability interpretation

Robert Oeckl

Full-text: Open access

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 space-time 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 space-time symmetries into the framework. We show how the Schrödinger–Feynman approach is a suitable starting point for casting quantum field theories into the general boundary form. We discuss the role of operators.

Article information

Source
Adv. Theor. Math. Phys., Volume 12, Number 2 (2008), 319-352.

Dates
First available in Project Euclid: 6 May 2008

Permanent link to this document
https://projecteuclid.org/euclid.atmp/1210083227

Mathematical Reviews number (MathSciNet)
MR2399313

Zentralblatt MATH identifier
1210.81039

Citation

Oeckl, Robert. General boundary quantum field theory: Foundations and probability interpretation. Adv. Theor. Math. Phys. 12 (2008), no. 2, 319--352. https://projecteuclid.org/euclid.atmp/1210083227


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