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The propagator of a spinning particle in external Abelian field and in arbitrary dimensions is presented by means of a path integral. The problem has different solutions in even and odd dimensions. In even dimensions the representation is…
The goal of this paper is to derive a simple recursion that generates a sequence of fractions approximating $\sqrt[n]{k}$ with increasing accuracy. The recursion is defined in terms of a series of first-order non-linear difference equations…
We discuss new ideas for consideration of loop diagrams and angular integrals in $D$-dimensions in QCD. In case of loop diagrams, we propose the covariant formalism of expansion of tensorial loop integrals into the orthogonal basis of…
We introduce a class of self-interacting scalar theories in which the various coupling contants obey a recursive relation. These imply a particularly simple form for the generating function of the Feynman amplitudes with vanishing external…
We derive an off-shell recursion relation for correlators that holds at all loop orders. This allows us to prove how generalized amplitudes transform under generic field redefinitions, starting from an assumed behavior of the…
A semi-analytic method is proposed for the generation of realizations of a multivariate process of a given linear correlation structure and marginal distribution. This is an extension of a similar method for univariate processes,…
With the help of mathematical technique of irreducible tensors the multipole expansion for the probability amplitude of spontaneous radiation of a quantum system is derived. It is shown that the found series represents the total radiation…
We construct the action-angle variables of a classical integrable model defined on complex projective phase space and calculate the quantum mechanical propagator in the coherent state path integral representation using the stationary phase…
We introduce a growth process which samples sections of uniform infinite causal triangulations by elementary moves in which a single triangle is added. A relation to a random walk on the integer half line is shown. This relation is used to…
Complex-valued semiclassical methods hold out the promise of treating classically allowed and classically forbidden processes on the same footing. In addition, they provide a natural way to describe optical excitation with complex fields…
New algorithms for construction of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes with finite phase spaces are presented. These algorithms are based on a special technique of sequential…
We generalize the quantum random walk protocol for a particle in a one-dimensional chain, by using several types of biased quantum coins, arranged in aperiodic sequences, in a manner that leads to a rich variety of possible wave function…
We construct the most general form of our previously proposed nonlinear extension of quantum mechanics that possesses three basic properties. Unlike the simpler model, the new version is not completely integrable, but it has an underlying…
Non--minimal repulsive singularities (``repulsons'') in extended supergravity theories are investigated. The short distance antigravity properties of the repulsons are tested at the classical and the quantum level by a scalar…
This work explores the non-relativistic quantum propagator $K(x,t)$ as a solution of the Schr\"odinger equation. We suppose that the propagator takes the form ${\rm exp}\left(\frac{\mathrm{i}}{\hbar}S+R\right)$, generalizing the usual WKB…
Generative modeling using samples drawn from the probability distribution constitutes a powerful approach for unsupervised machine learning. Quantum mechanical systems can produce probability distributions that exhibit quantum correlations…
An extensive number of numerical computations of energy 1/$N$ series using a recursive Taylor series method are presented in this paper. The series are computed to a high order of approximation and their behaviour on increasing the order of…
This paper suggests a new way to compute the path integral for simple quantum mechanical systems. The new algorithm originated from previous research in string theory. However, its essential simplicity is best illustrated in the case of a…
Time dependence for barrier penetration is considered in the phase space. An asymptotic phase-space propagator for nonrelativistic scattering on a one - dimensional barrier is constructed. The propagator has a form universal for various…
In this paper we suggest a simple mathematical procedure to derive the classical probability density of quantum systems via Bohr's correspondence principle. Using Fourier expansions for the classical and quantum distributions, we assume…