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 $SO(3)$ Yang-Mills-Higgs theory, where we prove that the asymptotic symmetry group is $Z_{|m|}\times \Re$ where $m$ 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 $SO(3)$ to $SU(2)$.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

On Galilei Invariance in Quantum Mechanics and the Bargmann Superselection Rule

We reinvestigate Bargmann's superselection rule for the overall mass of $n$ particles in ordinary quantum mechanics with Galilei invariant interaction potential. We point out that in order for mass to define a superselection rule it should be considered as a dynamical variable. We present a minimal extension of the original dynamics in which mass it treated as dynamical variable. Here the classical symmetry group turns out to be given by an $\reals$-extension of the Galilei group which formerly appeared only at the quantum level. There is now no obstruction to implement an action of the classical symmetry group on Hilbert space. We include some critical comments of a general nature on formal derivations of superselection rules without dynamical context.Comment: 14 Pages, Plain-TeX, no figure