Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Annalen der Physik

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

R.A. Frick

Published Nov 20, 2008• 0 citations
Publisher

Abstract

Abstract In a generalized Heisenberg/Schrödinger 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.

DOI
10.1002/andp.20085201205

Related papers

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

R.A. Frick

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.

arXiv:hep-th/0602104•Annalen der Physik•Nov 20, 2008•4 citations

The de Broglie Wave as Evidence of a Deeper Wave Structure

Daniel Shanahan

It is argued that the de Broglie wave is not the wave usually supposed, but the relativistically induced modulation of an underlying carrier wave that moves with the velocity of the particle. In the rest frame of the particle this underlying structure has the form of a standing wave. De Broglie also assumed the existence of this antecedent standing wave, but it would appear that he failed to notice its survival as a carrier wave in the Lorentz transformed wave structure. Identified as a modulation, the de Broglie wave acquires a physically reasonable ontology, evidencing a more natural unity between matter and radiation than might otherwise be contemplated, and avoiding the necessity of recovering the particle velocity from a superposition of such waves. Because the Schrödinger and other wave equations for massive particles were conceived as equations for the de Broglie wave, this interpretation of the wave is also relevant to such issues in quantum mechanics as the meaning of the wave function, the nature of wave-particle duality, and the possibility of well-defined particle trajectories.

arXiv:1503.02534•Mar 6, 2015•0 citations

Propagator for a spin 1/2 particle in terms of the unitary representations of the Lorentz group

R.A. Frick

In this paper we extend our previous result on the description of the partcle motion in a generalized Heisenberg picture to a relativistic fermion. The operators of the Lorentz algebra in this picture may be regarded as field operators. In this approach the transition amplitudes for the particle are constructed in terms of two-component functions in the unitary representations of the Lorentz group.

arXiv:hep-th/0203034•Mar 5, 2002•0 citations

The representations of the Lorentz group in quantum mechanics

J. M. Jauch, Christian Frønsdal, H.A. Tolhoek +1 more

•Jan 1, 1959•1 citation

Chapter 18. De Broglie Waves Lead to the Momentum Operator

Dennis Morris

De Gruyter eBooks•May 27, 2016•0 citations

A new Hamilton operator for a massive relativistic particle with spin one in a generalized Heisenberg/Schrödinger picture

R.A. Frick

We consider a particular four-dimensional generalization of the transition from the Heisenberg to the Schrödinger picture. The space–time independent expansion with respect to the unitary irreducible representations of the Lorentz group is applied, as Fourier transformation in the Heisenberg picture, to the states of a massive relativistic particle. A new Hamilton operator has been found for such a particle with spin one.

arXiv:hep-th/9612212•Journal of Mathematical Physics•Jul 1, 1997•2 citations
Abstract In a generalized Heisenberg/Schrödinger 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.
It is argued that the de Broglie wave is not the wave usually supposed, but the relativistically induced modulation of an underlying carrier wave that moves with the velocity of the particle. In the rest frame of the particle this underlying structure has the form of a standing wave. De Broglie also assumed the existence of this antecedent standing wave, but it would appear that he failed to notice its survival as a carrier wave in the Lorentz transformed wave structure. Identified as a modulation, the de Broglie wave acquires a physically reasonable ontology, evidencing a more natural unity between matter and radiation than might otherwise be contemplated, and avoiding the necessity of recovering the particle velocity from a superposition of such waves. Because the Schrödinger and other wave equations for massive particles were conceived as equations for the de Broglie wave, this interpretation of the wave is also relevant to such issues in quantum mechanics as the meaning of the wave function, the nature of wave-particle duality, and the possibility of well-defined particle trajectories.