112 research outputs found
Noncanonical quantization of gravity. II. Constraints and the physical Hilbert space
The program of quantizing the gravitational field with the help of affine
field variables is continued. For completeness, a review of the selection
criteria that singles out the affine fields, the alternative treatment of
constraints, and the choice of the initial (before imposition of the
constraints) ultralocal representation of the field operators is initially
presented. As analogous examples demonstrate, the introduction and enforcement
of the gravitational constraints will cause sufficient changes in the operator
representations so that all vestiges of the initial ultralocal field operator
representation disappear. To achieve this introduction and enforcement of the
constraints, a well characterized phase space functional integral
representation for the reproducing kernel of a suitably regularized physical
Hilbert space is developed and extensively analyzed.Comment: LaTeX, 42 pages, no figure
Metrical Quantization
Canonical quantization may be approached from several different starting
points. The usual approaches involve promotion of c-numbers to q-numbers, or
path integral constructs, each of which generally succeeds only in Cartesian
coordinates. All quantization schemes that lead to Hilbert space vectors and
Weyl operators---even those that eschew Cartesian coordinates---implicitly
contain a metric on a flat phase space. This feature is demonstrated by
studying the classical and quantum ``aggregations'', namely, the set of all
facts and properties resident in all classical and quantum theories,
respectively. Metrical quantization is an approach that elevates the flat phase
space metric inherent in any canonical quantization to the level of a
postulate. Far from being an unwanted structure, the flat phase space metric
carries essential physical information. It is shown how the metric, when
employed within a continuous-time regularization scheme, gives rise to an
unambiguous quantization procedure that automatically leads to a canonical
coherent state representation. Although attention in this paper is confined to
canonical quantization we note that alternative, nonflat metrics may also be
used, and they generally give rise to qualitatively different, noncanonical
quantization schemes.Comment: 13 pages, LaTeX, no figures, to appear in Born X Proceeding
Impurity-induced dephasing of Andreev states
A study is presented concerning the influence of flicker noise in the
junction transparency on coherent transport in Andreev states. The amount of
dephasing is estimated for a microwave-activated quantum interferometer.
Possibilities of experimentally investigating the coupling between a
superconducting quantum point contact and its electromagnetic environment are
discussed.Comment: 8 pages, 4 figure
Gazeau-Klauder type coherent states for hypergeometric type operators
The hypergeometric type operators are shape invariant, and a factorization
into a product of first order differential operators can be explicitly
described in the general case. Some additional shape invariant operators
depending on several parameters are defined in a natural way by starting from
this general factorization. The mathematical properties of the eigenfunctions
and eigenvalues of the operators thus obtained depend on the values of the
involved parameters. We study the parameter dependence of orthogonality, square
integrability and of the monotony of eigenvalue sequence. The obtained results
allow us to define certain systems of Gazeau-Klauder coherent states and to
describe some of their properties. Our systematic study recovers a number of
well-known results in a natural unified way and also leads to new findings.Comment: An error occurring in Theorem 12 and Theorem 13 has been correcte
Spin tunneling and topological selection rules for integer spins
We present topological interference effects for the tunneling of a single
large spin, which are caused by the symmetry of a general class of magnetic
anisotropies. The interference originates from spin Berry phases associated
with different tunneling paths exposed to the same dynamics. Introducing a
generalized path integral for coherent spin states, we evaluate transition
amplitudes between ground as well as low-lying excited states. We show that
these interference effects lead to topological selection rules and spin-parity
effects for integer spins that agree with quantum selection rules and which
thus provide a generalization of the Kramers degeneracy to integer spins. Our
results apply to the molecular magnets Mn12 and Fe8.Comment: 4 pages, 3 EPS figures, REVTe
Complex Langevin: Etiology and Diagnostics of its Main Problem
The complex Langevin method is a leading candidate for solving the so-called
sign problem occurring in various physical situations. Its most vexing problem
is that in some cases it produces `convergence to the wrong limit'. In the
first part of the paper we go through the formal justification of the method,
identify points at which it may fail and identify a necessary and sufficient
criterion for correctness. This criterion would, however, require checking
infinitely many identities, and therefore is somewhat academic. We propose
instead a truncation to the check of a few identities; this still gives a
necessary criterion, but a priori it is not clear whether it remains
sufficient. In the second part we carry out a detailed study of two toy models:
first we identify the reasons why in some cases the method fails, second we
test the efficiency of the truncated criterion and find that it works perfectly
at least in the toy models studied.Comment: 39 pages, 15 figures; typos corrected and reference adde
Coherent states for exactly solvable potentials
A general algebraic procedure for constructing coherent states of a wide
class of exactly solvable potentials e.g., Morse and P{\"o}schl-Teller, is
given. The method, {\it a priori}, is potential independent and connects with
earlier developed ones, including the oscillator based approaches for coherent
states and their generalizations. This approach can be straightforwardly
extended to construct more general coherent states for the quantum mechanical
potential problems, like the nonlinear coherent states for the oscillators. The
time evolution properties of some of these coherent states, show revival and
fractional revival, as manifested in the autocorrelation functions, as well as,
in the quantum carpet structures.Comment: 11 pages, 4 eps figures, uses graphicx packag
Sampling Theorem and Discrete Fourier Transform on the Riemann Sphere
Using coherent-state techniques, we prove a sampling theorem for Majorana's
(holomorphic) functions on the Riemann sphere and we provide an exact
reconstruction formula as a convolution product of samples and a given
reconstruction kernel (a sinc-type function). We also discuss the effect of
over- and under-sampling. Sample points are roots of unity, a fact which allows
explicit inversion formulas for resolution and overlapping kernel operators
through the theory of Circulant Matrices and Rectangular Fourier Matrices. The
case of band-limited functions on the Riemann sphere, with spins up to , is
also considered. The connection with the standard Euler angle picture, in terms
of spherical harmonics, is established through a discrete Bargmann transform.Comment: 26 latex pages. Final version published in J. Fourier Anal. App
Smooth Paths on Three Dimensional Lattice
A particular class of random walks with a spin factor on a three dimensional
cubic lattice is studied. This three dimensional random walk model is a simple
generalization of random walk for the two dimensional Ising model. All critical
diffusion constants and associated critical exponents are calculated. Continuum
field theories such as Klein-Gordon, Dirac and massive Chern-Simons theories
are constructed near several critical points.Comment: 7 pages,NUP-A-94-
Field theoretic approach to metastability in the contact process
A quantum field theoretic formulation of the dynamics of the Contact Process
on a regular graph of degree z is introduced. A perturbative calculation in
powers of 1/z of the effective potential for the density of particles phi(t)
and an instantonic field psi(t) emerging from the quantum formalism is
performed. Corrections to the mean-field distribution of densities of particles
in the out-of-equilibrium stationary state are derived in powers of 1/z.
Results for typical (e.g. average density) and rare fluctuation (e.g. lifetime
of the metastable state) properties are in very good agreement with numerical
simulations carried out on D-dimensional hypercubic (z=2D) and Cayley lattices.Comment: Final published version; 20 pages, 5 figure
- …