Abstract
We develop a notion of quantum observable for the general boundary formulation of quantum theory. This notion is adapted to spacetime regions rather than to hypersurfaces and naturally fits into the topological-quantum-field-theory-like axiomatic structure of the general boundary formulation. We also provide a proposal for a generalized concept of expectation value adapted to this type of observable. We show how the standard notion of quantum observable arises as a special case together with the usual expectation values. We proceed to introduce various quantization schemes to obtain such quantum observables including path integral quantization (yielding the time-ordered product), Berezin-Toeplitz (antinormal-ordered) quantization and normal-ordered quantization, and discuss some of their properties.
Mathematics Subject Classification (2010). Primary 81P15; Secondary 81P16, 81T70, 53D50, 81S40, 81R30.
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Oeckl, R. (2012). Observables in the General Boundary Formulation. In: Finster, F., Müller, O., Nardmann, M., Tolksdorf, J., Zeidler, E. (eds) Quantum Field Theory and Gravity. Springer, Basel. https://doi.org/10.1007/978-3-0348-0043-3_8
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DOI: https://doi.org/10.1007/978-3-0348-0043-3_8
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