Physics
Scientific paper
Nov 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986phrvd..34.3044k&link_type=abstract
Physical Review D (Particles and Fields), Volume 34, Issue 10, 15 November 1986, pp.3044-3057
Physics
43
Gauge Field Theories, Canonical Formalism, Lagrangians, And Variational Principles
Scientific paper
Gauge systems described in the preceding paper are canonically quantized in a way which is manifestly covariant under all transformations relevant in the classical theory. Special observables are represented by scalar differential operators acting on the space scrF of C∞(scrM,C ) functions on the ``big'' configuration manifold scrM. Physical states Ψ∈scrF0 are annihilated by all operators υ^ representing the elements υ of the gauge algebra scrV. The inner product in scrF0 is based on the measure provided by the physical metric induced by the Hamiltonian. Special quantum observables are self-adjoint on the resulting Hilbert space scrH0. Factor ordering of such observables, based on their split into standard physical and gauge parts, is self-consistent. In particular, all special quantum observables commute with the constraints υ^ on the physical space scrF0 and hence can be considered as operators on scrF0. The Hamilton operator does not evolve the states out of the physical Hilbert space. These results are corroborated by an explicit evaluation of all commutators among special observables on the big function space scrF. Both the factor ordering and the construction of the inner product are ultimately cast into language which does not require the splitting of observables.
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