Local Well-Posedness of the Cauchy Problem for a $$p$$-Adic Nagumo-Type Equation

Chacón-Cortés, L. F.; Garcia-Bibiano, C. A.; Zúñiga–Galindo, W. A.

doi:10.1134/s2070046622040021

Cited by 1 publication

(1 citation statement)

References 31 publications

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“…The results about the space H 1 Q 3 ℘ are just variations of well-known results about ℘-adic Sobolev spaces; see, e.g. [53, section 10.2], [56], and the references therein.…”

Section: Some Function Spacesmentioning

confidence: 73%

℘ -adic quantum mechanics, the Dirac equation, and the violation of Einstein causality

Zúñiga-Galindo

2024

J. Phys. A: Math. Theor.

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This article studies the breaking of the Lorentz symmetry at the Planck length in quantum mechanics. We use three-dimensional ℘ -adic vectors as position variables, while the time remains a real number. In this setting, the Planck length is 1 / ℘ , where ℘ is a prime number, and the Lorentz symmetry is naturally broken. In the framework of the Dirac-von Neumann formalism for quantum mechanics, we introduce a new ℘ -adic Dirac equation that predicts the existence of particles and antiparticles and charge conjugation like the standard one. The discreteness of the ℘ -adic space imposes substantial restrictions on the solutions of the new equation. This equation admits localized solutions, which is impossible in the standard case. We show that an isolated quantum system whose evolution is controlled by the ℘ -adic Dirac equation does not satisfy the Einstein causality, which means that the speed of light is not the upper limit for the speed at which conventional matter or energy can travel through space. The new ℘ -adic Dirac equation is not intended to replace the standard one; it should be understood as a new version (or a limit) of the classical equation at the Planck length scale.

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“…The results about the space H 1 Q 3 ℘ are just variations of well-known results about ℘-adic Sobolev spaces; see, e.g. [53, section 10.2], [56], and the references therein.…”

Section: Some Function Spacesmentioning

confidence: 73%

℘ -adic quantum mechanics, the Dirac equation, and the violation of Einstein causality

Zúñiga-Galindo

2024

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

Local Well-Posedness of the Cauchy Problem for a $$p$$-Adic Nagumo-Type Equation

Cited by 1 publication

References 31 publications

℘ -adic quantum mechanics, the Dirac equation, and the violation of Einstein causality

℘ -adic quantum mechanics, the Dirac equation, and the violation of Einstein causality

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