Deformed Heisenberg algebra and minimal length

Abstract

A one-dimensional deformed Heisenberg algebra $[X,P]=if(P)$ is studied. We answer the question: For what function of deformation $f(P)$ there exists a nonzero minimal uncertainty in position (minimal length). We also find an explicit expression for the minimal length in the case of arbitrary function of deformation.

to be published in JPA

References in corpus (6)

• Hydrogen-atom spectrum under a minimal-length hypothesis
• Minimal Length Uncertainty Relation and gravitational quantum well
• Minimal Length and Bouncing Particle Spectrum
• Corrections to the ns-levels of hydrogen atom in deformed space with minimal length
• Singular inverse square potential in arbitrary dimensions with a minimal length: Application to the motion of a dipole in a cosmic string background
• The quantum N-body problem with a minimal length

Cited by in corpus (14)

• Minimum-length deformed QM/QFT, issues and problems
• One-dimensional Coulomb-like problem in general case of deformed space with minimal length
• Field propagation in a stochastic background space: The rate of light incoherence in stellar interferometry
• Relation of deformed nonlinear algebras with linear ones
• Exact solutions for two-body problems in 1D deformed space with minimal length
• Position and momentum uncertainties of a particle in a V-shaped potential under the minimal length uncertainty relation
• New version of pseudo-hermiticity in the two-sided deformation of Heisenberg algebra
• Kinetic energy properties and weak equivalence principle in a space with GUP
• New Deformed Heisenberg Algebra from the $\mu$-Deformed Model of Dark Matter
• Extra-dimensional generalization of minimum-length deformed QM/QFT and some of its phenomenological consequences
• Regularization of ${\delta }^{\prime }$ potential in general case of deformed space with minimal length
• Pseudo-Hermitian position and momentum operators, Hermitian Hamiltonian, and deformed oscillators
• Exact continuity equation in a space with minimal length
• Operator Ordering in the Relativistic Quantization: Specific Heat in the Rindler Frame