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03 October 2022
  » arxiv » gr-qc/0212023

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Note on Canonical Quantization and Unitary Equivalence in Field Theory
Alejandro Corichi ; Jeronimo Cortez ; Hernando Quevedo ;
Date 5 Dec 2002
Journal Class.Quant.Grav. 20 (2003) L83
Subject gr-qc hep-th
AbstractThe problem of defining and constructing representations of the Canonical Commutation Relations can be systematically approached via the technique of {it algebraic quantization}. In particular, when the phase space of the system is linear and finite dimensional, the `vertical polarization’ provides an unambiguous quantization. For infinite dimensional field theory systems, where the Stone-von Neumann theorem fails to be valid, even the simplest representation, the Schroedinger functional picture has some non-trivial subtleties. In this letter we consider the quantization of a real free scalar field --where the Fock quantization is well understood-- on an arbitrary background and show that the representation coming from the most natural application of the algebraic quantization approach is not, in general, unitary equivalent to the corresponding Schroedinger-Fock quantization. We comment on the possible implications of this result for field quantization.
Source arXiv, gr-qc/0212023
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