Related papers: Quantization and Semiclassics
Bifurcations of classical orbits introduce divergences into semiclassical spectra which have to be smoothed with the help of uniform approximations. We develop a technique to extract individual energy levels from semiclassical spectra…
The classical time of arrival in the interacting case is quantized by way of quantizing its expansion about the free time of arrival. The quantization is formulated in coordinate representation which represents ordering rules in terms of…
We present a list of formulae useful for Weyl-Heisenberg integral quantizations, with arbitrary weight, of functions or distributions on the plane. Most of these formulae are known, others are original. The list encompasses particular cases…
In this work we explain the relevance of the Differential Galois Theory in the semiclassical (or WKB) quantification of some two degree of freedom potentials. The key point is that the semiclassical path integral quantification around a…
We compute the partition function and specific heat for a quantum mechanical particle under the influence of a quartic double-well potential non-perturbatively, using the semiclassical method. Near the region of bounded motion in the…
Closed orbit theory is generalized to the semiclassical calculation of cross-correlated recurrence functions for atoms in external fields. The cross-correlation functions are inverted by a high resolution spectral analyzer to obtain the…
After an overview of the physical motivations for studying quantum gravity, we reprint THE FORMAL STRUCTURE OF QUANTUM GRAVITY, i.e. the 1978 Cargese Lectures by Professor B.S. DeWitt, with kind permission of Springer. The reader is…
The transfer operator due to Bogomolny provides a convenient method for obtaining a semiclassical approximation to the energy eigenvalues of a quantum system, no matter what the nature of the analogous classical system. In this paper, the…
The aim of this manuscript is to give some basic notions related to numerical semigroups, and from these on the one hand describe a classical application to the study of singularities of plane algebraic curves, and on the other, show how…
A pseudoclassical model to describe Weyl particle in 10 dimensions is proposed. In course of quantization both the massless Dirac equation and the Weyl condition are reproduced automatically. The construction can be relevant to…
In this paper we give examples of applications of general methods of quantization by symmetrization of classical integrable systems, which have been illustrated in two previous works by the same authors. We consider two classes of systems…
We present some basic inequalities between the classical and quantum values of free energy, entropy and mean energy. We investigate the transition from the deterministic case (classical mechanics) to the probabilistic case (quantum…
We investigate the possibility that the semiclassical limit of quantum mechanics might be correctly described by a classical dynamical theory, other than standard classical mechanics. Using a set of classicality criteria proposed in a…
This is the second part of a series devoting to the generalizations and applications of common theorems in variational bifurcation theory. Using abstract theorems in the first part we obtain many new bifurcation results for quasi-linear…
I briefly review some of the recent progress in quantum field theory in curved spacetime and other aspects of semiclassical gravity, as reported at the D3 Workshop at GR15.
Since the very early days of quantum theory there have been numerous attempts to interpret quantum mechanics as a statistical theory. This is equivalent to describing quantum states and ensembles together with their dynamics entirely in…
We classify the derivations of degree-one generalized Weyl algebras over a univariate Laurent polynomial ring. In particular, our results cover the Weyl-Hayashi algebra, a quantization of the first Weyl algebra arising as a primitive factor…
We have developed a semiclassical approach to solving the Bogoliubov - de Gennes equations for superconductors. It is based on the study of classical orbits governed by an effective Hamiltonian corresponding to the quasiparticles in the…
We study ring of functions on the (classical and quantized) phase space of 2-dimensional BF theory with the gauge group $\mathrm{GL}_N$ coupled to a 1-dimensional quantum mechanics with global symmetry $\mathrm{GL}_K$. These functions are…
The purpose of this contribution is to give an introduction to quantum geometry and loop quantum gravity for a wide audience of both physicists and mathematicians. From a physical point of view the emphasis will be on conceptual issues…