Observables in the General Boundary Formulation
arXiv:1101.0367 · doi:10.1007/978-3-0348-0043-3_8
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.
20 pages, LaTeX + AMS + birkjour (included), contribution to the proceedings of the conference "Quantum Field Theory and Gravity" (Regensburg, 2010); v2: minor corrections
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- The new spin foam models and quantum gravity
- The Unruh Effect in General Boundary Quantum Field Theory
- Locality and General Vacua in Quantum Field Theory
- Quantum field theory on timelike hypersurfaces in Rindler space
- Towards state locality in quantum field theory: free fermions
- The Unruh-deWitt Detector and the Vacuum in the General Boundary formalism
- (2+1) Lorentzian quantum cosmology from spin-foams: opportunities and obstacles for semi-classicality
- General Boundary Quantum Field Theory in Anti de Sitter Spacetimes
- Cylinder topological quantum field theory: A categorical presentation of classical field theory and its symmetries