Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-09-15
Adv.Theor.Math.Phys.12:319-352,2008
Physics
High Energy Physics
High Energy Physics - Theory
30 pages, 5 figures, LaTeX; v2: typos corrected, footnote and remark added, references added/updated; v3: more typos corrected
Scientific paper
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.
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