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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 | | Abstract: | The 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 | | Services: | Forum | Review | PDF | Favorites | |
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