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We introduce a new p-adic Dirac equation that predicts the existence ofparticles and antiparticles and charge conjugation like the standard one. Thenew equation shares many properties with the old one. However, the space'sdiscrete (p-adic) nature imposes substantial restrictions on the solutions ofthe new equation. This equation admits localized solutions, which is impossiblein the standard case. Finally, we show that a quantum system whose evolution iscontrolled by the p-adic Dirac equation does not satisfy the Einsteincausality.

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