Observables in the general boundary formulation. (English) Zbl 1246.81019
Finster, Felix (ed.) et al., Quantum field theory and gravity. Conceptual and mathematical advances in the search for a unified framework. Papers based on the presentations at the conference, Regensburg, Germany, September 28 to October 1, 2010. Berlin: Springer (ISBN 978-3-0348-0042-6/hbk; 978-3-0348-0043-3/ebook). 137-156 (2012).
Summary: 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.
For the entire collection see [Zbl 1234.81017].
For the entire collection see [Zbl 1234.81017].
MSC:
| 81P15 | Quantum measurement theory, state operations, state preparations |
| 81P16 | Quantum state spaces, operational and probabilistic concepts |
| 81T70 | Quantization in field theory; cohomological methods |
| 53D50 | Geometric quantization |
| 81S40 | Path integrals in quantum mechanics |
| 81R30 | Coherent states |
