Matter waves in terms of the unitary representations of the Lorentz group

TL;DR

This paper explores how unitary Lorentz group representations can be used to describe matter waves, introducing an extended wavelength concept for massive particles within a generalized quantum framework.

Contribution

It introduces a novel approach linking Lorentz group representations to matter wave properties, extending the de Broglie wavelength concept in a generalized quantum setting.

Findings

Waves can have longer wavelengths than de Broglie waves for massive particles.

Propagators are defined as spacetime transitions between Lorentz Casimir eigenstates.

The approach offers a new perspective on relativistic quantum wave descriptions.

Abstract

In a generalized Heisenberg/Schroedinger picture, the unitary representations of the Lorentz group may, for a massive relativistic particle, be used to attribute to waves an extra wavelength that is longer than the de Broglie wavelength. Propagators are defined as spacetime transitions between states with different eigenvalues of the first or the second Casimir operator of the Lorentz algebra.