Related papers: Effective constrained polymeric theories and their…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
We consider a single particle which is bound by a central potential and obeys the Dirac equation in d dimensions. We first apply the asymptotic iteration method to recover the known exact solutions for the pure Coulomb case. For a…
Constrained Hamiltonian description of the classical limit is utilized in order to derive consistent dynamical equations for hybrid quantum-classical systems. Starting with a compound quantum system in the Hamiltonian formulation conditions…
We present an implementation of Wilson's renormalization group and a continuum limit tailored for loop quantization. The dynamics of loop quantized theories is constructed as a continuum limit of dynamics of effective theories. After…
A linear constraint loop is specified by a system of linear inequalities that define the relation between the values of the program variables before and after a single execution of the loop body. In this paper we consider the problem of…
We analyze the evolution of the effective potential and the particle spectrum of two-parameter families of non-integrable quantum field theories. These theories are defined by deformations of conformal minimal models M_m by using the…
In the present contribution we discuss the role of experimental limitations in the classical limit problem. We studied some simple models and found that Quantum Mechanics does not re-produce classical mechanical predictions, unless we…
We study sequences of solutions to the inhomogeneous Landau-Fermi-Dirac equation with Coulomb potential in which the quantum parameter converges to zero. Our main result establishes the compactness of these sequences, which allows us to…
we show there exists a mathematically consistent framework in which the Renormalization Program can be understood in a natural manner. The framework does not require any violations of mathematical rigor usually associated with the…
The apparent difficulty in recovering classical nonlinear dynamics and chaos from standard quantum mechanics has been the subject of a great deal of interest over the last twenty years. For open quantum systems - those coupled to a…
Lienard systems are very important mathematical models describing oscillatory processes arising in applied sciences. In this paper, we study polynomial Lienard systems of arbitrary degree on the plane, and develop a new method to obtain a…
The Dirac equation is solved for a pseudoscalar Coulomb potential in a two-dimensional world. An infinite sequence of bounded solutions are obtained. These results are in sharp contrast with those ones obtained in 3+1 dimensions where no…
We introduce a simple deformed quantization prescription that interpolates the classical and quantum sectors of Weinberg's nonlinear quantum theory. The result is a novel classical limit where $\hbar$ is kept fixed while a dimensionless…
The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem for the spherical anharmonic oscillator and the screened Coulomb potential is developed. Based upon the $\hbar$-expansions and suitable…
Despite its great successes in accounting for the current observations, the so called `standard' model of cosmology faces a number of fundamental unresolved questions. Paramount among these are those relating to the nature of the origin of…
In classical mechanics, external constraints on the dynamical variables can be easily implemented within the Lagrangian formulation. Conversely, the extension of this idea to the quantum realm, which dates back to Dirac, has proven…
We derive the effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) in the asymptotic limit where the restoring forces tend to infinity. In contrast to…
Recently a number of analytic prescriptions for computing the non-linear matter power spectrum have appeared in the literature. These typically involve resummation or closure prescriptions which do not have a rigorous error control, thus…
We review one dimensional matrix theory and its variations, collective field theory and quantum phase space description. In the planar limit, these theories become classical and can be easily analyzed. With these descriptions, one…
Semiclassical states in isotropic loop quantum cosmology are employed to show that the improved dynamics has the correct classical limit. The effective Hamiltonian for the quantum cosmological model with a massless scalar field is thus…