# Minimal length and generalized Dirac equation

@article{Nozari2005MinimalLA,
title={Minimal length and generalized Dirac equation},
author={Kourosh Nozari and Mojdeh Karami},
journal={Modern Physics Letters A},
year={2005},
volume={20},
pages={3095-3103}
}
• Published 3 July 2005
• Physics
• Modern Physics Letters A
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.
Generalized Dirac Equation for a particle in a gravitational field
• Physics
General Relativity and Gravitation
• 2021
The existence of a minimal observable length modifies the Heisenberg’s uncertainty principle at Plank scales and leads to some modifications of the Dirac equation. Here, we consider the generalized
Free Motion of a Dirac Particle with a Minimum Uncertainty in Position
In this paper, we present a covariant, relativistic noncommutative algebra which includes two small deformation parameters. Using this algebra, we obtain a generalized uncertainty principle which
Dirac equation in the curved spacetime and generalized uncertainty principle: A fundamental quantum mechanical approach with energy-dependent potentials
Abstract.In this work, we have obtained the solutions of the (1 + 1)-dimensional Dirac equation on a gravitational background within the generalized uncertainty principle. We have shown that how
Generalized Dirac equation and its symmetries
Existence of a minimal observable distance on the order of Planck length is an immediate consequence of the Generalized Uncertainty Principle (GUP). As a result, relativistic quantum mechanics should
Dirac equation from the extended uncertainty principle
• Physics
Physica Scripta
• 2021
The existence of a minimal momentum modifies the Heisenberg’s uncertainty principle, which implies modifications of the Dirac equation. In this work, we study the influence of this minimal
Generalized relativistic harmonic oscillator in minimal length quantum mechanics
• Physics, Mathematics
• 2016
We solve the generalized relativistic harmonic oscillator in 1+1 dimensions in the presence of a minimal length. Using the momentum space representation, we explore all the possible signs of the
Path Integral for Dirac oscillator with generalized uncertainty principle
• Physics
• 2012
The propagator for Dirac oscillator in (1+1) dimension, with deformed commutation relation of the Heisenberg principle, is calculated using path integral in quadri-momentum representation. As the
Particles of Spin Zero and 1/2 in Electromagnetic Field with Confining Scalar Potential in Modified Heisenberg Algebra
• Physics
• 2015
In this paper, we propose to solve the relativistic Klein Gordon and Dirac equations subjected to the action of a uniform electomagnetic field confining scalar potential yin the presence of a minimal
A generalized bosonic oscillator in the presence of a minimal length
• Physics
• 2010
We present an exact solution of the three-dimensional Duffin–Kemmer–Petiau oscillator for spins 1 and 0 in the momentum space with the presence of minimal length uncertainty by the technique of
Relativistic particle in electromagnetic fields with a generalized uncertainty principle
• Physics
• 2012
In this paper, we propose to solve the relativistic Klein–Gordon and Dirac equations subjected to the action of a uniform electromagnetic field with a generalized uncertainty principle in the

## References

SHOWING 1-10 OF 61 REFERENCES
MINIMUM PHYSICAL LENGTH AND THE GENERALIZED UNCERTAINTY PRINCIPLE IN STRING THEORY
• Physics
• 1990
A possible definition of path integrals for string theory is studied, based on a discretized version of Polyakov's generating functional. The finite resolution of string theory, as opposed to the
Hilbert space representation of the minimal length uncertainty relation.
• Kempf, Mann
• Physics, Medicine
Physical review. D, Particles and fields
• 1995
The quantum mechanical structure which underlies the generalized uncertainty relation which quantum theoretically describes the minimal length as a minimal uncertainty in position measurements is studied.
Particle theories with minimum observable length and open string theory
Abstract We investigate a class of particle theories that have minimum observable length. Among them we find the theory equivalent to the open bosonic string theory. For this theory, starting from a
A generalized uncertainty principle in quantum gravity
We discuss a Gedanken experiment for the measurement of the area of the apparent horizon of a black hole in quantum gravity. Using rather general and model-independent considerations we find a
The algebraic structure of the generalized uncertainty principle
We show that a deformation of the Heisenberg algebra which depends on a dimensionful parameter κ is the algebraic structure which underlies the generalized uncertainty principle in quantum gravity.
Quantum groups, gravity, and the generalized uncertainty principle.
• Maggiore
• Physics, Medicine
Physical review. D, Particles and fields
• 1994
The result indicates that in the $\ensuremath{\kappa}$-deformed Poincar\'e algebra a minimal observable length emerges naturally.
Quantum Gravity and Minimum Length
The existence of a fundamental scale, a lower bound to any output of a position measurement, seems to be a model-independent feature of quantum gravity. In fact, different approaches to this theory
Generalized Uncertainty Principle in Quantum Gravity from Micro-Black Hole Gedanken Experiment
Abstract We review versions of the Generalized Uncertainty Principle (GUP) obtained in string theory and in gedanken experiments carried out in quantum gravity. We show how a GUP can be derived from
A Stringy Nature Needs Just Two Constants
Dual string theories of everything, being purely geometrical, contain only two fundamental constants: c, for relativistic invariance, and a length λ, for quantization. Planck's and Newton's constants
Minimal length uncertainty relation and the hydrogen atom
We propose a new approach to calculate perturbatively the effects of a particular deformed Heisenberg algebra on an energy spectrum. We use this method to calculate the harmonic oscillator spectrum