Implications of minimum-length deformed quantum mechanics for QFT/QG

Abstract

After picking out what may seem more realistic minimal gravitational deformation of quantum mechanics, we study its back reaction on gravity. The large distance behaviour of Newtonian potential coincides with the result obtained by using of effective field theory approach to general relativity (the correction proves to be of repulsive nature). The short distance corrections result in Planck mass black hole remnants with zero temperature. The deformation of position-momentum uncertainty relations leads to the superluminal motion that can be avoided by making similar deformation of time-energy uncertainty relation. Such deformation also avoids UV divergences in QFT.

12 pages, 2 figures, Extended version of the talk delivered at the workshop dedicated to S. G. Matinyan's 80th birthday, 28-29 September, 2011, Tbilisi; will appear in Fortschritte der Physik

References in corpus (8)

• Black hole quantum tunnelling and black hole entropy correction
• Multi-Particle States in Deformed Special Relativity
• Power Spectrum of the Density Perturbations From Smooth Hybrid New Inflation Model
• Regular black holes in UV self-complete quantum gravity
• Effective Field Theory of Gravity: Leading Quantum Gravitational Corrections to Newtons and Coulombs Law
• Solving the Effective Field Equations for the Newtonian Potential
• Gravity in quantum spacetime
• Macroscopic Screening of Coulomb Potentials From UV/IR-Mixing

Cited by in corpus (8)

• Minimal Length Scale Scenarios for Quantum Gravity
• The Compton-Schwarzschild correspondence from extended de Broglie relations
• Minimum-length deformed QM/QFT, issues and problems
• Minimum length, extra dimensions, modified gravity and black hole remnants
• Black hole remnants due to Planck-length deformed QFT
• Deformed Hamilton-Jacobi Method in Covariant Quantum Gravity Effective Models
• Extra-dimensional generalization of minimum-length deformed QM/QFT and some of its phenomenological consequences
• Homogeneous Field and WKB Approximation In Deformed Quantum Mechanics with Minimal Length