p-Adic Quantum Mechanics, the Dirac Equation, and the violation of Einstein causality

Authors

Wilson A. Zuniga-Galindo, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

2024

Abstract

We introduce a new p-adic Dirac equation that predicts the existence of particles and antiparticles and charge conjugation like the standard one. The new equation shares many properties with the old one. However, the space's discrete (p-adic) nature imposes substantial restrictions on the solutions of the new equation. This equation admits localized solutions, which is impossible in the standard case. Finally, we show that a quantum system whose evolution is controlled by the p-adic Dirac equation does not satisfy the Einstein causality.

Recommended Citation

Zúñiga-Galindo, W. A. "p-Adic Quantum Mechanics, the Dirac Equation, and the violation of Einstein causality." arXiv preprint arXiv:2312.02744 (2023).