Relativistic Generalized Uncertainty Principle
arXiv:1810.11761 · doi:10.1016/j.aop.2019.03.014
Abstract
The Generalized Uncertainty Principle and the related minimum length are normally considered in non-relativistic Quantum Mechanics. Extending it to relativistic theories is important for having a Lorentz invariant minimum length and for testing the modified Heisenberg principle at high energies.In this paper, we formulate a relativistic Generalized Uncertainty Principle. We then use this to write the modified Klein-Gordon, Schrödinger and Dirac equations, and compute quantum gravity corrections to the relativistic hydrogen atom, particle in a box, and the linear harmonic oscillator.
6 pages, Revtex
References in corpus (7)
- Interpretation of Quantum Field Theories with a Minimal Length Scale
- Lorentz-covariant deformed algebra with minimal length
- Potential tests of the Generalized Uncertainty Principle in the advanced LIGO experiment
- Generalized uncertainty principles and quantum field theory
- Rigorous Hamiltonian and Lagrangian analysis of classical and quantum theories with minimal length
- Spin exchange dominated by charge fluctuations of the Wigner lattice in the newly synthesized chain cuprate Na5Cu3O6
- Topological Defects in a Deformed Gauge Theory
Cited by in corpus (36)
- Quantum gravitational decoherence from fluctuating minimal length and deformation parameter at the Planck scale
- 30 years in: Quo vadis generalized uncertainty principle?
- Generalized uncertainty principle with maximal observable momentum and no minimal length indeterminacy
- Modified commutators are not sufficient to determine a quantum gravity minimal length scale
- Quantum field theory with the generalized uncertainty principle I: scalar electrodynamics
- Gravitationally induced uncertainty relations in curved backgrounds
- Maximal momentum GUP leads to quadratic gravity
- Quantum field theory with the generalized uncertainty principle II: Quantum Electrodynamics
- Discreteness of Space from GUP in Strong Gravitational Fields
- Effective GUP-modified Raychaudhuri equation and black hole singularity: four models
- Gravitational effects on the Heisenberg Uncertainty Principle: a geometric approach
- Relativistic Extended Uncertainty Principle from Spacetime Curvature
- Minimal and maximal lengths from position-dependent noncommutativity
- Non-commutative space engine: a boost to thermodynamic processes
- A novel mechanism for probing the Planck scale
- Quantum gravitational signatures in next-generation gravitational wave detectors
- Reinterpreting deformed Heisenberg algebras
- Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
- Constraining the generalized uncertainty principle with neutron interferometry
- Quantum Cycle in Relativistic Non-Commutative Space with Generalized Uncertainty Principle correction
- Covariant version of Pauli Hamiltonian, spin-induced non commutativity, Thomas precession and precession of spin
- The solitary solutions of nonlinear Klein-Gordon field with minimal length
- The dominating mode of two competing massive modes of quadratic gravity
- A covariant tapestry of linear GUP, metric-affine gravity, their Poincaré algebra and entropy bound
- Constraints on General Relativity Geodesics by a Covariant Geometric Uncertainty Principle
- Quantum corrections in general relativity explored through a GUP-inspired maximal acceleration analysis
- Covariant Space Time Line Elements in the Friedmann Lemaitre Robertson Walker Geometry
- Generalized Uncertainty Principle: from the harmonic oscillator to a QFT toy model
- Lorentz-covariant sampling theory for fields
- Non-local imprints of gravity on quantum theory
- GUP, Lorentz Invariance (Non)-Violation, and Non-Commutative Geometry
- A novel mechanism for probing the Planck scale with wavepackets following general distributions
- Quantum Non-demolition Measurements in the Relativistic Dirac Oscillator
- UV Effects and Short-Lived Hawking Radiation: Alternative Resolution of Information Paradox
- Relativistic generalised uncertainty and the corrected vacuum energy
- Minimal length implications on the Hartree-Fock theory