Parametrized Relativistic Quantum Theory

Peter Schwerdtfeger

John R. Fanchi

A probabilistic basis for Parametrized Relativistic Quantum Theory (PRQT) has been developed for multicomponent eigenvectors and many-body applications in flat spacetime. This paper presents an extension of the multicomponent, many-body PRQT formalism to curved spacetime.

James E. Dodd, Ben M. Gripaios

James B. Hartle

The `evolving constants' method of defining the quantum dynamics of time-reparametrization-invariant theories is investigated for a particular implementation of parametrized non-relativistic quantum mechanics (PNRQM). The wide range of time functions that are available to define evolving constants raises issues of interpretation, consistency, and the degree to which the resulting quantum theory coincides with, or generalizes, the usual non-relativistic theory. The allowed time functions must be restricted for the predictions of PNRQM to coincide with those of usual quantum theory. They must be restricted to have a notion of quantum evolution in a time parameter connected to spacetime geometry. They must be restricted to prevent the theory from making inconsistent predictions for the probabilities of histories. Suitable restrictions can be introduced in PNRQM but these seem unlikely to apply to a reparametrization-invariant theory like general relativity.

Detlef Dürr, Dustin Lazarovici

John R. Fanchi

Parametrized Relativistic Quantum Theory (PRQT) extends conventional relativistic quantum mechanics by introducing an invariant evolution parameter (s) and a broader symmetry group. This paper presents the axiomatic and probabilistic foundations of PRQT. The resulting Stueckelberg equation is applied to the study of barrier penetration, with explicit calculations for scanning tunneling microscopy (STM). The STM application demonstrates high sensitivity to barrier width and quantitative agreement between exact and thick-barrier approximations.