Minimal Length and Generalized Dirac Equation

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.

arXiv comment10 pages, no figure

References in corpus (16)

• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Quantum gravity and minimum length
• A Generalized Uncertainty Principle in Quantum Gravity
• Generalized Uncertainty Principle in Quantum Gravity from Micro-Black Hole Gedanken Experiment
• The Generalized Uncertainty Principle and Black Hole Remnants
• The algebraic structure of the generalized uncertainty principle
• Quantum Groups, Gravity, and the Generalized Uncertainty Principle
• On Gravity and the Uncertainty Principle
• Minimal Length Uncertainty Relation and Hydrogen Atom
• Signatures in the Planck Regime
• Generalized Uncertainty Principle, Extra-dimensions and Holography
• Some Consequences of the Generalised Uncertainty Principle: Statistical Mechanical, Cosmological, and Varying Speed of Light
• Minimal Length Uncertainty Relation and the Hydrogen Spectrum
• Gravitational Uncertainty and Black Hole Remnants
• Probing the minimal length scale by precision tests of the muon g-2
• Generalized Uncertainty Principle and Quantum Electrodynamics

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• 30 years in: Quo vadis generalized uncertainty principle?
• Fermion's tunnelling with effects of quantum gravity
• Implications of Minimal Length Scale on the Statistical Mechanics of Ideal Gas
• Remarks on remnants by fermions' tunnelling from black strings
• Near horizon thermodynamics of hairy black holes from gravitational decoupling
• Quantum gravity correction to Hawking radiation of the 2+1 dimensional wormhole
• Failure of Standard Thermodynamics in Planck Scale Black Hole System
• Quantum Gravity Effect on the Tunneling Particles from 2+1 dimensional New-type Black Hole
• Generalized relativistic harmonic oscillator in minimal length quantum mechanics
• Quantum tunneling from high dimensional Gödel black hole
• The GUP effect on tunnelling of massive vector bosons from the 2+1 dimensional black hole
• Dirac $\delta$-function potential in quasiposition representation of a minimal-length scenario
• Charged fermions tunneling from stationary axially symmetric black holes with generalized uncertainty principle
• Schwinger's Model of Angular Momentum with GUP
• Massless Charged Particles Tunneling Radiation from a RN-dS Horizon and the Linear and Quadratic GUP
• Exotic fermionic fields and minimal length
• Relativistic Approach to the Hydrogen Atom in a Minimal Length Scenario
• Free Motion of a Dirac Particle with a Minimum Uncertainty in Position
• Tunneling in ABC trilayer graphene superlattice
• Minimal length implications on the Hartree-Fock theory