Related papers: Path Integral for Relativistic Dionium System
An adaptive, kink-based path integral formalism is used to calculate the ground state energies of the atoms He-Ne. The method uses an adaptive scheme to virtually eliminate the sign difficulties. This is done by using a Monte Carlo scheme…
A path-integral approach for delta-function potentials is presented. Particular attention is paid to the two-dimensional case, which illustrates the realization of a quantum anomaly for a scale invariant problem in quantum mechanics. Our…
Path integrals have, over the years, proven to be an extremely versatile tool for simulating the dynamics of open quantum systems. The initial limitations of applicability of these methods in terms of the size of the system has steadily…
A full symmetry classification is given for models of energy transport in radiant plasma when the mass density is spatially variable and the diffusivity is nonlinear. A systematic search for conservation laws also leads to some potential…
A model of a relativistic particle moving in the Liouville field is investigated. Symmetry group of the system is $SL(2,R)/Z_2$. The corresponding dynamical integrals describe full set of classical trajectories. Dynamical integrals are used…
We discuss a relativistic theory of the atomic nuclei in the framework of the hamiltonian formalism and of the mesonic model of the nucleus. Attention is paid to the translational invariance of the theory. Our approach is centered on the…
The collision operator for a relativistic plasma is reformulated in terms of an expansion in spherical harmonics. In this formulation the collision operator is expressed in terms of five scalar potentials which are given by one-dimensional…
Phase-space path-integrals are used in order to illustrate various aspects of a recently proposed interpretation of quantum mechanics as a gauge theory of metaplectic spinor fields.
This work addresses the quantization of a self-interacting higher order time derivative theory using path integrals. To quantize this system and avoid the problems of energy not bounded from below and states of negative norm, we observe the…
We present a derivation of the Schr\"odinger equation for a path integral of a point particle in a space with curvature and torsion which is considerably shorter and more elegant than what is commonly found in the literature.
We derive the partition function of a non-relativistic quantum string which its ends are allowed to freely slide on the two angled straight solid rods. We first derive the classical solution of the model and then use it to derive the…
A general and rigorous methodology to compute the quantum equilibrium isotope effect is described. Unlike standard approaches, ours does not assume separability of rotational and vibrational motions and does not make the harmonic…
We briefly review a hamiltonian path integral formalism developed earlier by one of us. An important feature of this formalism is that the path integral quantization in arbitrary co-ordinates is set up making use of only classical…
It is shown, that in the general case the Kustaanheimo-Stiefel transformation (reduction of $4d$ oscillator on the twistor space by the Hamiltonian action of $U(1)$ with further time-reparametrization) leads to the integrable system,…
The Loschmidt echo is a measure of quantum irreversibility and is determined by the fidelity amplitude of an imperfect time-reversal protocol. Fidelity amplitude plays an important role both in the foundations of quantum mechanics and its…
We make use of point transformations to introduce new canonical variables for systems defined on a finite interval and on the half-line so that new position variables should take all real values from $-\infty$ to $\infty$. The completeness…
Feynman's path integral is generalized to quantum mechanics on p-adic space and time. Such p-adic path integral is analytically evaluated for quadratic Lagrangians. Obtained result has the same form as that one in ordinary quantum…
Feynman's path integral approach is studied in the framework of the Wigner-Dunkl deformation of quantum mechanics. We start with reviewing some basics from Dunkl theory and investigate the time evolution of a Gaussian wave packet, which…
We derive an $su(1,1)$ coherent state path integral formula for a system of two one-dimensional anyons in a harmonic potential. By a change of variables we transform this integral into a coherent states path integral for a harmonic…
This book provides an introduction to path integral methods and their application to modeling atomistic processes. The book covers both the foundational theory and recently developed simulation techniques. The text provides a self-contained…