575 research outputs found
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
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-
On Galilei Invariance in Quantum Mechanics and the Bargmann Superselection Rule
We reinvestigate Bargmann's superselection rule for the overall mass of
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 -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
On the Construction of Time-Symmetric Black Hole Initial Data
We review in a pedagogical fashion the 3+1-split which serves to put
Einstein's equations into the form of a dynamical system with constraints. We
then discuss the constraint equations under the simplifying assumption of
time-symmetry. Multi-Black-Hole data are presented and more explicitly
described in the case of two holes. The effect of different topologies is
emphasized.Comment: 18 pages, Latex, uses Springer style-file lamuphys.sty. To appear in
"Black Holes: Theory and Observation", edited by F. Hehl, C. Kiefer and R.
Metzler, Springer 199
The Generalized Thin-Sandwich Problem and its Local Solvability
We consider Einstein Gravity coupled to dynamical matter consisting of a
gauge field with any compact gauge group and minimally coupled scalar fields.
We investigate the conditions under which a free specification of a spatial
field configuration for the total system and its derivative with respect to
coordinate-time determines a solution to the field equations (generalized
thin-sandwich problem). Sufficient conditions for local solvability (in the
space of fields) are established.Comment: 18 pages, Plain Te
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