Minimal Length and Generalized Dirac Equation
Kourosh Nozari, Mojdeh Karami
TL;DR
This paper derives a modified Dirac equation incorporating a minimal length scale suggested by string theory and quantum gravity, showing that free particles cannot exist at the Planck scale due to spacetime fluctuations.
Contribution
It introduces a new form of the Dirac equation accounting for minimal length effects and solves its eigenvalue problem for free particles.
Findings
Modified Dirac equation incorporating minimal length
Free particles cannot exist at the Planck scale
Spacetime fluctuations prevent free particles at quantum gravity scales
Abstract
Existence of a minimal observable length which has been indicated by string theory and quantum gravity, leads to a modification of Dirac equation. In this letter we find this modified Dirac equation and solve its eigenvalue problem for a free particle. We will show that due to background spacetime fluctuation, it is impossible to have free particle in Planck scale.
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