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April 2008 General boundary quantum field theory: Foundations and probability interpretation
Robert Oeckl
Adv. Theor. Math. Phys. 12(2): 319-352 (April 2008).


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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Robert Oeckl. "General boundary quantum field theory: Foundations and probability interpretation." Adv. Theor. Math. Phys. 12 (2) 319 - 352, April 2008.


Published: April 2008
First available in Project Euclid: 6 May 2008

zbMATH: 1210.81039
MathSciNet: MR2399313

Rights: Copyright © 2008 International Press of Boston


Vol.12 • No. 2 • April 2008
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