743 research outputs found
SO(4) Invariant States in Quantum Cosmology
The phenomenon of linearisation instability is identified in models of
quantum cosmology that are perturbations of mini-superspace models. In
particular, constraints that are second order in the perturbations must be
imposed on wave functions calculated in such models. It is shown explicitly
that in the case of a model which is a perturbation of the mini-superspace
which has spatial sections these constraints imply that any wave
functions calculated in this model must be SO(4) invariant. (This replaces the
previous corrupted version.)Comment: 15 page
Inequivalent Quantizations of Gauge Theories
It is known that the quantization of a system defined on a topologically
non-trivial configuration space is ambiguous in that many inequivalent quantum
systems are possible. This is the case for multiply connected spaces as well as
for coset spaces. Recently, a new framework for these inequivalent
quantizations approach has been proposed by McMullan and Tsutsui, which is
based on a generalized Dirac approach. We employ this framework for the
quantization of the Yang-Mills theory in the simplest fashion. The resulting
inequivalent quantum sectors are labelled by quantized non-dynamical
topological charges.Comment: 24 pages, LaTeX, to be publ. in Int.J.Mod.Phys.
On the existence of Killing vector fields
In covariant metric theories of coupled gravity-matter systems the necessary
and sufficient conditions ensuring the existence of a Killing vector field are
investigated. It is shown that the symmetries of initial data sets are
preserved by the evolution of hyperbolic systems.Comment: 9 pages, no figure, to appear in Class. Quant. Gra
Stratification of the orbit space in gauge theories. The role of nongeneric strata
Gauge theory is a theory with constraints and, for that reason, the space of
physical states is not a manifold but a stratified space (orbifold) with
singularities. The classification of strata for smooth (and generalized)
connections is reviewed as well as the formulation of the physical space as the
zero set of a momentum map. Several important features of nongeneric strata are
discussed and new results are presented suggesting an important role for these
strata as concentrators of the measure in ground state functionals and as a
source of multiple structures in low-lying excitations.Comment: 22 pages Latex, 1 figur
On the existence of star products on quotient spaces of linear Hamiltonian torus actions
We discuss BFV deformation quantization of singular symplectic quotient
spaces in the special case of linear Hamiltonian torus actions. In particular,
we show that the Koszul complex on the moment map of an effective linear
Hamiltonian torus action is acyclic. We rephrase the nonpositivity condition of
Arms, Gotay and Jennings for linear Hamiltonian torus actions. It follows that
reduced spaces of such actions admit continuous star products.Comment: 9 pages, 4 figures, uses psfra
A gauge model for quantum mechanics on a stratified space
In the Hamiltonian approach on a single spatial plaquette, we construct a
quantum (lattice) gauge theory which incorporates the classical singularities.
The reduced phase space is a stratified K\"ahler space, and we make explicit
the requisite singular holomorphic quantization procedure on this space. On the
quantum level, this procedure furnishes a costratified Hilbert space, that is,
a Hilbert space together with a system which consists of the subspaces
associated with the strata of the reduced phase space and of the corresponding
orthoprojectors. The costratified Hilbert space structure reflects the
stratification of the reduced phase space. For the special case where the
structure group is , we discuss the tunneling probabilities
between the strata, determine the energy eigenstates and study the
corresponding expectation values of the orthoprojectors onto the subspaces
associated with the strata in the strong and weak coupling approximations.Comment: 38 pages, 9 figures. Changes: comments on the heat kernel and
coherent states have been adde
The York map as a Shanmugadhasan canonical transformation in tetrad gravity and the role of non-inertial frames in the geometrical view of the gravitational field
A new parametrization of the 3-metric allows to find explicitly a York map in
canonical ADM tetrad gravity, the two pairs of physical tidal degrees of
freedom and 14 gauge variables. These gauge quantities (generalized inertial
effects) are all configurational except the trace of
the extrinsic curvature of the instantaneous 3-spaces (clock
synchronization convention) of a non-inertial frame. The Dirac hamiltonian is
the sum of the weak ADM energy (whose density is coordinate-dependent due to the inertial
potentials) and of the first-class constraints. Then: i) The explicit form of
the Hamilton equations for the two tidal degrees of freedom in an arbitrary
gauge: a deterministic evolution can be defined only in a completely fixed
gauge, i.e. in a non-inertial frame with its pattern of inertial forces. ii) A
general solution of the super-momentum constraints, which shows the existence
of a generalized Gribov ambiguity associated to the 3-diffeomorphism gauge
group. It influences: a) the explicit form of the weak ADM energy and of the
super-momentum constraint; b) the determination of the shift functions and then
of the lapse one. iii) The dependence of the Hamilton equations for the two
pairs of dynamical gravitational degrees of freedom (the generalized tidal
effects) and for the matter, written in a completely fixed 3-orthogonal
Schwinger time gauge, upon the gauge variable ,
determining the convention of clock synchronization. Therefore it should be
possible (for instance in the weak field limit but with relativistic motion) to
try to check whether in Einstein's theory the {\it dark matter} is a gauge
relativistic inertial effect induced by .Comment: 90 page
Experience with a fluorescenceâbased beam position monitor at the APS
We have recently redesigned the first crystal mount of our cryogenically cooled monochromator to reduce its sensitivity to pressure fluctuations in the cryogenic lines feeding the Si (111) crystal. With the use of a fluorescenceâbased Xâray beam position monitor (BPM) placed 19 m away from the monochromator, much operational experience has been gained on the sensitivity of the beam position and intensity to small changes in the cooling system. In this presentation, we will describe our Xâray BPM design and performance and will provide examples of changes that have made the beam position more stable on our beamline. One such change for example has been the topâup operation of the Advanced Photon Source (APS), which has reduced the thermal drifts associated with the ring current decay. © 2004 American Institute of PhysicsPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87659/2/679_1.pd
Proof of the Thin Sandwich Conjecture
We prove that the Thin Sandwich Conjecture in general relativity is valid,
provided that the data satisfy certain geometric
conditions. These conditions define an open set in the class of possible data,
but are not generically satisfied. The implications for the ``superspace''
picture of the Einstein evolution equations are discussed.Comment: 8 page
Renaissance of the ~1 TeV Fixed-Target Program
This document describes the physics potential of a new fixed-target program
based on a ~1 TeV proton source. Two proton sources are potentially available
in the future: the existing Tevatron at Fermilab, which can provide 800 GeV
protons for fixed-target physics, and a possible upgrade to the SPS at CERN,
called SPS+, which would produce 1 TeV protons on target. In this paper we use
an example Tevatron fixed-target program to illustrate the high discovery
potential possible in the charm and neutrino sectors. We highlight examples
which are either unique to the program or difficult to accomplish at other
venues.Comment: 31 pages, 11 figure
- âŠ