On the Implementation of Constraints through Projection Operators

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dc.creatorKempf, A.
dc.creatorKlauder, J. R.
dc.date2000-09-19
dc.date.accessioned2026-07-07T10:54:57Z
dc.date.available2026-07-07T10:54:57Z
dc.descriptionQuantum constraints of the type Q ψ= 0 can be straightforwardly implemented in cases where Q is a self-adjoint operator for which zero is an eigenvalue. In that case, the physical Hilbert space is obtained by projecting onto the kernel of Q, i.e. H_phys = ker(Q) = ker(Q*). It is, however, nontrivial to identify and project onto H_phys when zero is not in the point spectrum but instead is in the continuous spectrum of Q, because in this case the kernel of Q is empty. Here, we observe that the topology of the underlying Hilbert space can be harmlessly modified in the direction perpendicular to the constraint surface in such a way that Q becomes non-self-adjoint. This procedure then allows us to conveniently obtain H_phys as the proper Hilbert subspace H_phys = ker(Q*), on which one can project as usual. In the simplest case, the necessary change of topology amounts to passing from an L^2 Hilbert space to a Sobolev space.
dc.description22 pages, LaTeX
dc.identifierhttps://arxiv.org/abs/quant-ph/0009072
dc.identifierhttp://arxiv.org/abs/quant-ph/0009072
dc.identifierJ.Phys.A34:1019-1036,2001
dc.identifierdoi:10.1088/0305-4470/34/5/307
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/185971
dc.subjectQuantum Physics
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleOn the Implementation of Constraints through Projection Operators
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