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

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Quaternionic Dirac equation

A. J. Davies

Published Apr 15, 1990• 91 citations
Publisher

Abstract

The quaternionic generalization of the Dirac equation is investigated. From elementary considerations of unitarity and Lorentz invariance it is demonstrated that potentials with quaternionic parts are not consistent with representation independence. This result leads to the conclusion that either quaternionic quantum mechanics singles out a special class of Dirac representations, or that allowed potentials appearing in the problem have no j or k components. If the latter alternative is the case, consideration of nonrelativistic wave mechanics casts doubt on the existence of simple experimental tests of quaternionic quantum mechanics.

DOI
10.1103/physrevd.41.2628

Related papers

A ONE-COMPONENT DIRAC EQUATION

Stefano De Leo

We develop a relativistic free wave equation on the complexified quaternions, linear in the derivatives. Even if the wave functions are only one-component, we show that four independent solutions, corresponding to those of the Dirac equation, exist. A partial set of translations between complex and complexified quaternionic quantum mechanics may be defined.

arXiv:hep-th/9508010•International Journal of Modern Physics A•Aug 20, 1996•27 citations

Quantum Dynamics in Regions of Quaternionic Curvature

Steven P. Brumby, Gayatri Joshi

The complex unit appearing in the equations of quantum mechanics is generalised to a quaternionic structure on spacetime, leading to the consideration of complex quantum mechanical particles whose dynamical behaviour is governed by inhomogeneous Dirac and Schrödinger equations. Mixing of hyper-complex components of wavefunctions occurs through their interaction with potentials dissipative into the extra quaternionic degrees of freedom. An interferometric experiment is analysed to illustrate the effect.

arXiv:hep-th/9406191•Jun 29, 1994•0 citations

Scattering Study of Fermions due to Double Dirac Delta Potential in Quaternionic Relativistic Quantum Mechanics

HASSAN HASSANABADI, Hadi Sobhani, Won Sang Chung

We have studied the scattering problem of relativistic fermions from a quaternionic double Dirac delta potential. We have used Dirac equation in the presence of the scalar and vector potentials in the quaternionic formalism of relativistic quantum mechanics to study the problem. The wave functions of different regions have been derived. Then, using the reflection coefficient, transmission coefficient, and the continuity equation, the scattering problem has been investigated in detail. It has been shown that we have faced some fluctuations in the reflection and transmission coefficients.

arXiv:1709.09941•Advances in High Energy Physics•Jan 1, 2018•18 citations

Scattering in quantum mechanics under quaternionic Dirac delta potential

Hadi Sobhani, HASSAN HASSANABADI

In this paper, the Schrödinger equation for quaternionic quantum mechanics with a Dirac delta potential has been investigated. The derivative discontinuity condition for the quaternionic wave function has been derived and the boundary conditions for the quaternionic wave function have been applied. Probability current densities for different regions of the problem have been determined along with reflection and transmission coefficients.

Canadian Journal of Physics•Dec 4, 2015•30 citations

Relativistic scattering of fermions in quaternionic quantum mechanics

HASSAN HASSANABADI, Hadi Sobhani, A. Banerjee

In this article, we propose a quaternionic version of the Dirac equation in the presence of scalar and vector potentials. It has been shown that in complex limit of such an equation, the complex version of this equation can be covered. After setting a quaternionic form for the Dirac delta potential, scattering due to the considered interaction has been studied. Wave functions and discontinuity conditions of the problem considered have been derived in detail. Using the continuity equation, we have found a constraint implying the conservation law of the probability current.

The European Physical Journal C•Sep 1, 2017•30 citations

Self-interacting quantum particles and the Dirac delta potential

Sergio Giardino

The Dirac delta function potential is considered within the real Hilbert space approach for complex wave functions, as well as quaternionic wave functions. As has been previously determined, the real Hilbert space approach enables the possibility of self-interacting physical systems. The self-interaction precludes confining states, and also imposes non-stationary quantum states, both of them representing novel situations that cannot be observed in terms of quantum wave functions. These results remark the differences between quaternionic quantum mechanics ($\mathbbm H$QM) and complex quantum mechanics ($\mathbbm C$QM), and also establish a method of solving the wave equation that may be applied to a variety of different cases.

quant-pharXiv:2511.14424•Brazilian Journal of Physics•Nov 19, 2025•2 citations
The quaternionic generalization of the Dirac equation is investigated. From elementary considerations of unitarity and Lorentz invariance it is demonstrated that potentials with quaternionic parts are not consistent with representation independence. This result leads to the conclusion that either quaternionic quantum mechanics singles out a special class of Dirac representations, or that allowed potentials appearing in the problem have no j or k components. If the latter alternative is the case, consideration of nonrelativistic wave mechanics casts doubt on the existence of simple experimental tests of quaternionic quantum mechanics.
The complex unit appearing in the equations of quantum mechanics is generalised to a quaternionic structure on spacetime, leading to the consideration of complex quantum mechanical particles whose dynamical behaviour is governed by inhomogeneous Dirac and Schrödinger equations. Mixing of hyper-complex components of wavefunctions occurs through their interaction with potentials dissipative into the extra quaternionic degrees of freedom. An interferometric experiment is analysed to illustrate the effect.
We have studied the scattering problem of relativistic fermions from a quaternionic double Dirac delta potential. We have used Dirac equation in the presence of the scalar and vector potentials in the quaternionic formalism of relativistic quantum mechanics to study the problem. The wave functions of different regions have been derived. Then, using the reflection coefficient, transmission coefficient, and the continuity equation, the scattering problem has been investigated in detail. It has been shown that we have faced some fluctuations in the reflection and transmission coefficients.
In this article, we propose a quaternionic version of the Dirac equation in the presence of scalar and vector potentials. It has been shown that in complex limit of such an equation, the complex version of this equation can be covered. After setting a quaternionic form for the Dirac delta potential, scattering due to the considered interaction has been studied. Wave functions and discontinuity conditions of the problem considered have been derived in detail. Using the continuity equation, we have found a constraint implying the conservation law of the probability current.
The Dirac delta function potential is considered within the real Hilbert space approach for complex wave functions, as well as quaternionic wave functions. As has been previously determined, the real Hilbert space approach enables the possibility of self-interacting physical systems. The self-interaction precludes confining states, and also imposes non-stationary quantum states, both of them representing novel situations that cannot be observed in terms of quantum wave functions. These results remark the differences between quaternionic quantum mechanics ($\mathbbm H$QM) and complex quantum mechanics ($\mathbbm C$QM), and also establish a method of solving the wave equation that may be applied to a variety of different cases.