Advances in Theoretical and Mathematical Physics

General boundary quantum field theory: Foundations and probability interpretation

Robert Oeckl

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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.

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

First available in Project Euclid: 6 May 2008

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Oeckl, Robert. General boundary quantum field theory: Foundations and probability interpretation. Adv. Theor. Math. Phys. 12 (2008), no. 2, 319--352.

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