705 research outputs found
Geometry and symmetries of multi-particle systems
The quantum dynamical evolution of atomic and molecular aggregates, from
their compact to their fragmented states, is parametrized by a single
collective radial parameter. Treating all the remaining particle coordinates in
d dimensions democratically, as a set of angles orthogonal to this collective
radius or by equivalent variables, bypasses all independent-particle
approximations. The invariance of the total kinetic energy under arbitrary
d-dimensional transformations which preserve the radial parameter gives rise to
novel quantum numbers and ladder operators interconnecting its eigenstates at
each value of the radial parameter.
We develop the systematics and technology of this approach, introducing the
relevant mathematics tutorially, by analogy to the familiar theory of angular
momentum in three dimensions. The angular basis functions so obtained are
treated in a manifestly coordinate-free manner, thus serving as a flexible
generalized basis for carrying out detailed studies of wavefunction evolution
in multi-particle systems.Comment: 37 pages, 2 eps figure
The exit-time problem for a Markov jump process
The purpose of this paper is to consider the exit-time problem for a
finite-range Markov jump process, i.e, the distance the particle can jump is
bounded independent of its location. Such jump diffusions are expedient models
for anomalous transport exhibiting super-diffusion or nonstandard normal
diffusion. We refer to the associated deterministic equation as a
volume-constrained nonlocal diffusion equation. The volume constraint is the
nonlocal analogue of a boundary condition necessary to demonstrate that the
nonlocal diffusion equation is well-posed and is consistent with the jump
process. A critical aspect of the analysis is a variational formulation and a
recently developed nonlocal vector calculus. This calculus allows us to pose
nonlocal backward and forward Kolmogorov equations, the former equation
granting the various moments of the exit-time distribution.Comment: 15 pages, 7 figure
Spinning Braid Group Representation and the Fractional Quantum Hall Effect
The path integral approach to representing braid group is generalized for
particles with spin. Introducing the notion of {\em charged} winding number in
the super-plane, we represent the braid group generators as homotopically
constrained Feynman kernels. In this framework, super Knizhnik-Zamolodchikov
operators appear naturally in the Hamiltonian, suggesting the possibility of
{\em spinning nonabelian} anyons. We then apply our formulation to the study of
fractional quantum Hall effect (FQHE). A systematic discussion of the ground
states and their quasi-hole excitations is given. We obtain Laughlin, Halperin
and Moore-Read states as {\em exact} ground state solutions to the respective
Hamiltonians associated to the braid group representations. The energy gap of
the quasi-excitation is also obtainable from this approach.Comment: (36 pages) e-mail [email protected]
Half-Differentials and Fermion Propagators
From a geometric point of view, massless spinors in dimensions are
composed of primary fields of weights and ,
where the weights are defined with respect to diffeomorphisms of a sphere in
momentum space. The Weyl equation thus appears as a consequence of the
transformation behavior of local sections of half--canonical bundles under a
change of charts. As a consequence, it is possible to impose covariant
constraints on spinors of negative (positive) helicity in terms of
(anti--)holomorphy conditions. Furthermore, the identification with
half--differentials is employed to determine possible extensions of fermion
propagators compatible with Lorentz covariance. This paper includes in
particular the full derivation of the primary correlators needed in order to
determine the fermion correlators.Comment: 22 pages, Latex, IASSNS-HEP-94/8
Chiral Deformations of Conformal Field Theories
We study general perturbations of two-dimensional conformal field theories by
holomorphic fields. It is shown that the genus one partition function is
controlled by a contact term (pre-Lie) algebra given in terms of the operator
product expansion. These models have applications to vertex operator algebras,
two-dimensional QCD, topological strings, holomorphic anomaly equations and
modular properties of generalized characters of chiral algebras such as the
algebra, that is treated in detail.Comment: 28 pages, late
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