Towards a Proper Quantum Theory

Inge Svein Helland

Tepper L. Gill, Trey Morris, S. K. Kurtz

This paper is a progress report on the foundations for the canonical proper-time approach to relativistic quantum theory. We first review the the standard square-root equation of relativistic quantum theory, followed by a review of the Dirac equation, providing new insights into the physical properties of both. We then introduce the canonical proper-time theory. For completeness, we give a brief outline of the canonical proper-time approach to electrodynamics and mechanics, and then introduce the canonical proper-time approach to relativistic quantum theory. This theory leads to three new relativistic wave equations. In each case, the canonical generator of proper-time translations is strictly positive definite, so that it represents a particle. We show that the canonical proper-time extension of the Dirac equation for Hydrogen gives results that are consistently closer to the experimental data, when compared to the Dirac equation. However, these results are not sufficient to account for either the Lamb shift or the anomalous magnetic moment.

Hitoshi Wakita

Renormalizing the state vectors which represent the clouds of the proper fields of particles, we can define a new Hilbert space where the interaction Hamiltonian has a definite mathematical meaning. The success of the renormalization theory seems to show that the quantum theory of fields can be treated properly by using this new Hilbert space. Though this Hilbert space is not unique, states will be uniquely determined as linear functionals on some set of physical quantities. The clouds of the proper fields really exist, but they are not observed at all.

Inge Svein Helland

M. Ichiyanagi

We develop a formal theory which rests upon Nambu's description of the quantum state and especially on the use of the proper time. We show that the introduction of the proper time in quantum mechanics in understandable from the viewpoint that eligible trajectries in the well-known variational treatment of classical mechanics can be parametrized by an auxiliary variable. A new theory developed here permits a formulation of barrier penetrations in terms of the so-called Euclidean Lagrangian.

Stephen Bruce Sontz