2,632 research outputs found
Quantum mechanics on manifolds and topological effects
A unique classification of the topological effects associated to quantum
mechanics on manifolds is obtained on the basis of the invariance under
diffeomorphisms and the realization of the Lie-Rinehart relations between the
generators of the diffeomorphism group and the algebra of infinitely
differentiable functions on the manifold. This leads to a unique
("Lie-Rinehart") C* algebra as observable algebra; its regular representations
are shown to be locally Schroedinger and in one to one correspondence with the
unitary representations of the fundamental group of the manifold. Therefore, in
the absence of spin degrees of freedom and external fields, the first homotopy
group of the manifold appears as the only source of topological effects.Comment: A few comments have been added to the Introduction, together with
related references; a few words have been changed in the Abstract and a Note
added to the Titl
The Effect of \u3ci\u3eLaughlin v. Evanston Hospital\u3c/i\u3e on Consumer Fraud Act Claims for Nondeceptive Unfair Acts or Practices
Topology Classes of Flat U(1) Bundles and Diffeomorphic Covariant Representations of the Heisenberg Algebra
The general construction of self-adjoint configuration space representations
of the Heisenberg algebra over an arbitrary manifold is considered. All such
inequivalent representations are parametrised in terms of the topology classes
of flat U(1) bundles over the configuration space manifold. In the case of
Riemannian manifolds, these representations are also manifestly diffeomorphic
covariant. The general discussion, illustrated by some simple examples in non
relativistic quantum mechanics, is of particular relevance to systems whose
configuration space is parametrised by curvilinear coordinates or is not simply
connected, which thus include for instance the modular spaces of theories of
non abelian gauge fields and gravity.Comment: 22 pages, no figures, plain LaTeX file; changes only in details of
affiliation and financial suppor
Algebraic characterization of constraints and generation of mass in gauge theories
The possibility of non-trivial representations of the gauge group on
wavefunctionals of a gauge invariant quantum field theory leads to a generation
of mass for intermediate vector and tensor bosons. The mass parameters "m" show
up as central charges in the algebra of constraints, which then become of
second-class nature. The gauge group coordinates acquire dynamics outside the
null-mass shell and provide the longitudinal field degrees of freedom that
massless bosons need to form massive bosons.Comment: 4 pages, LaTeX, no figures; uses espcrc2.sty (twocolumn).
Contribution to the "Third Meeting on Constrained Dynamics and Quantum
Gravity QG99" held in Sardinia, Italy, on Sept. 1999. To appear in Nucl.
Phys. B (Proc. Suppl.
Predictions of ultra-harmonic oscillations in coupled arrays of limit cycle oscillators
Coupled distinct arrays of nonlinear oscillators have been shown to have a
regime of high frequency, or ultra-harmonic, oscillations that are at multiples
of the natural frequency of individual oscillators. The coupled array
architectures generate an in-phase high-frequency state by coupling with an
array in an anti-phase state. The underlying mechanism for the creation and
stability of the ultra-harmonic oscillations is analyzed. A class of
inter-array coupling is shown to create a stable, in-phase oscillation having
frequency that increases linearly with the number of oscillators, but with an
amplitude that stays fairly constant. The analysis of the theory is illustrated
by numerical simulation of coupled arrays of Stuart-Landau limit cycle
oscillators.Comment: 24 pages, 9 figures, accepted to Phys. Rev. E, in pres
- …