Urs Gerber's research while affiliated with Universidad Michoacana de San Nicolás de Hidalgo and other places
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Publications (4)
In recent years efficient algorithms have been developed for the numerical computation of relativistic single-particle path integrals in quantum field theory. Here, we adapt this “worldline Monte Carlo” approach to the standard problem of the numerical approximation of the non-relativistic path integral, resulting in a formalism whose characteristi...
In recent years efficient algorithms have been developed for the numerical computation of relativistic single-particle path integrals in quantum field theory. Here, we adapt this "worldline Monte Carlo" approach to the standard problem of the numerical approximation of the non-relativistic path integral, resulting in a formalism whose characteristi...
We introduce two new integral transforms of the quantum mechanical transition kernel that represent physical information about the path integral. These transforms can be interpreted as probability distributions on particle trajectories measuring respectively the relative contribution to the path integral from paths crossing a given spatial point (t...
We study the ground state energy and the critical screening parameter of the Yukawa potential in non-relativistic quantum mechanics. After a short review of the existing literature on these quantities, we apply fifth-order perturbation theory to the calculation of the ground state energy, using the exact solutions of the Coulomb potential together...
Citations
... These approaches are based on delta-like potentials instead of the method of images. On the other hand, worldline numerical computations have been employed on the same areas [10,12,[69][70][71], mostly considering rigid boundaries and scalar fields. The approach provided in the present article could be used to study these phenomena analytically for spinor fields, as well to test numerical computations in manifolds with rigid boundaries. ...
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... The worldline formalism has been successfully applied to several problems; see the book [52], the reviews [53,54] and references therein. In particular, it has recently proved useful in three situations that are relevant to the present computation: in phase space, where it has been applied to investigate noncommutative quantum field theories [55][56][57] and Berry phases [58], in the analysis of singular potentials and metrics [31,59,60] and in the study of boundaries [61][62][63][64] (see also [65][66][67] for related path-integral approaches). ...
... Some mathematical properties of the RSCP, e.g., the dilatation analyticity and Fourier analysis, have also attracted increasing interest in recent years [1,13]. In view of the extensive application of the conventional screened Coulomb potential in chemical physics [14], atomic and plasma physics [15][16][17][18], and condensed matter systems [19][20][21], the newly proposed RSCP may reveal its potential usefulness in these active areas. ...
