569 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-
Matter from Space
General Relativity offers the possibility to model attributes of matter, like
mass, momentum, angular momentum, spin, chirality etc. from pure space, endowed
only with a single field that represents its Riemannian geometry. I review this
picture of `Geometrodynamics' and comment on various developments after
Einstein.Comment: 37 Pages, 17 figures. Based on a talk delivered at the conference
"Beyond Einstein: Historical Perspectives on Geometry, Gravitation, and
Cosmology in the Twentieth Century", September 2008 at the University of
Mainz in Germany. To appear in the Einstein-Studies Series, Birkhaeuser,
Boston. v2: Reference [7] added and typo in formula [42] correcte
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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