2,596 research outputs found
Determination and Reduction of Large Diffeomorphisms
Within the Hamiltonian formulation of diffeomorphism invariant theories we
address the problem of how to determine and how to reduce diffeomorphisms
outside the identity component.Comment: 4 pages, Latex, macro espcrc2.sty. Contribution to the proceedings of
the second conference on Constrained Dynamics and Quantum Gravity, Santa
Margherita, Italy, 17-21 September 1996. To appear in Nucl. Phys. B Supp
Group Averaging and Refined Algebraic Quantization
We review the framework of Refined Algebraic Quantization and the method of
Group Averaging for quantizing systems with first-class constraints. Aspects
and results concerning the generality, limitations, and uniqueness of these
methods are discussed.Comment: 4 pages, LaTeX 2.09 using espcrc2.sty. To appear in the proceedings
of the third "Meeting on Constrained Dynamics and Quantum Gravity", Nucl.
Phys. B (Proc. Suppl.
Asymptotic Symmetry Groups of Long-Ranged Gauge Configurations
We make some general remarks on long-ranged configurations in gauge or
diffeomorphism invariant theories where the fields are allowed to assume some
non vanishing values at spatial infinity. In this case the Gauss constraint
only eliminates those gauge degrees of freedom which lie in the connected
component of asymptotically trivial gauge transformations. This implies that
proper physical symmetries arise either from gauge transformations that reach
to infinity or those that are asymptotically trivial but do not lie in the
connected component of transformations within that class. The latter
transformations form a discrete subgroup of all symmetries whose position in
the ambient group has proven to have interesting implications. We explain this
for the dyon configuration in the Yang-Mills-Higgs theory, where we
prove that the asymptotic symmetry group is where is
the monopole number. We also discuss the application of the general setting to
general relativity and show that here the only implication of discrete
symmetries for the continuous part is a possible extension of the rotation
group to .Comment: 14 pages, Plain TeX, Report CGPG-94/10-
Quantum Mechanics On Spaces With Finite Fundamental Group
We consider in general terms dynamical systems with finite-dimensional,
non-simply connected configuration-spaces. The fundamental group is assumed to
be finite. We analyze in full detail those ambiguities in the quantization
procedure that arise from the non-simply connectedness of the classical
configuration space. We define the quantum theory on the universal cover but
restrict the algebra of observables \O to the commutant of the algebra
generated by deck-transformations. We apply standard superselection principles
and construct the corresponding sectors. We emphasize the relevance of all
sectors and not just the abelian ones.Comment: 40 Pages, Plain-TeX, no figure
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