Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-01-01
Quantum Field Theory and Gravity (Regensburg, 2010), Birkh\"auser, Basel, 2012, pp. 137-156
Physics
High Energy Physics
High Energy Physics - Theory
20 pages, LaTeX + AMS + birkjour (included), contribution to the proceedings of the conference "Quantum Field Theory and Gravi
Scientific paper
10.1007/978-3-0348-0043-3_8
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.
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