arXiv subjects

Rafael Ferraro

Publications and source records attributed to Rafael Ferraro.

59 records · Page 4Linked to original sources

arXiv1999

The Jacobi principal function in Quantum Mechanics

The canonical functional action in the path integral in phase space is discretized by linking each pair of consecutive vertebral points --${\bf q}_k$ and ${\bf p}_{k+1}$ or ${\bf p}_k$ and ${\bf q}_{k+1}$-- through the invariant complete solution of the Hamilton-Jacobi equation associated with the classical path defined by these extremes. When the measure is chosen to reflect the geometrical character of the propagator (it must behave as a density of weight 1/2 in both of its arguments), the resulting infinitesimal propagator is cast in the form of an expansion in a basis of short-time solutions of the wave equation, associated with the eigenfunctions of the initial momenta canonically conjugated to a set of normal coordinates. The operator ordering induced by this prescription is a combination of a symmetrization rule coming from the phase, and a derivative term coming from the measure.

quant-ph↗

arXiv1997

BRST operator quantization of generally covariant gauge systems

The BRST generator is realized as a Hermitian nilpotent operator for a finite-dimensional gauge system featuring a quadratic super-Hamiltonian and linear supermomentum constraints. As a result, the emerging ordering for the Hamiltonian constraint is not trivial, because the potential must enter the kinetic term in order to obtain a quantization invariant under scaling. Namely, BRST quantization does not lead to the curvature term used in the literature as a means to get that invariance. The inclusion of the potential in the kinetic term, far from being unnatural, is beautifully justified in light of the Jacobi's principle.

hep-th↗

arXiv1996

The complete solution of the Hamilton-Jacobi equation in Quantum Mechanics

An ordinary unambiguous integral representation for the finite propagator of a quantum system is found by starting of a privileged skeletonization of the functional action in phase space, provided by the complete solution of the Hamilton-Jacobi equation. This representation allows to regard the propagator as the sum of the contributions coming from paths where the momenta generated by the complete solution of the Hamilton-Jacobi equation are conserved -as it does happen on the classical trajectory-, but are not restricted to having the classical values associated with the boundary conditions for the original coordinates.

quant-ph↗

arXiv1995

Canonical Gauges in the Path Integral for Parametrized Systems

It is well known that --differing from ordinary gauge systems-- canonical gauges are not admissible in the path integral for parametrized systems. This is the case for the relativistic particle and gravitation. However, a time dependent canonical transformation can turn a parametrized system into an ordinary gauge system. It is shown how to build a canonical transformation such that the fixation of the new coordinates is equivalent to the fixation of the original ones; this aim can be achieved only if the Hamiltonian constraint allows for an intrinsic global time. Thus the resulting action, describing an ordinary gauge system and allowing for canonical gauges, can be used in the path integral for the quantum propagator associated with the original variables.

hep-th↗

arXiv1995

Extrinsic Time in Quantum Cosmology

An extrinsic time is identified in most isotropic and homogeneous cosmological models by matching them with the ideal clock - a parametrized system whose only "degree of freedom" is time -. Once this matching is established, the cosmological models are quantized in the same way as the ideal clock. The space of solutions of the Wheeler-DeWitt equation is turned out into a Hilbert space by inserting a time dependent operator in the inner product, yielding a unitary theory equivalent to the phase space reduced theory.

gr-qc↗