The Casimir Effect in the Presence of a Minimal Length

Abstract

Large extra dimensions lower the Planck scale to values soon accessible. Not only is the Planck scale the energy scale at which effects of modified gravity become important. The Planck length also acts as a minimal length in nature, providing a natural ultraviolet cutoff and a limit to the possible resolution of spacetime. In this paper we examine the influence of the minimal length on the Casimir energy between two plates.

references and comment on the figure in section III added

References in corpus (41)

• The Hierarchy Problem and New Dimensions at a Millimeter
• New Dimensions at a Millimeter to a Fermi and Superstrings at a TeV
• Phenomenology, Astrophysics and Cosmology of Theories with Sub-Millimeter Dimensions and TeV Scale Quantum Gravity
• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Quantum gravity and minimum length
• Extra Spacetime Dimensions and Unification
• Grand Unification at Intermediate Mass Scales through Extra Dimensions
• Black Holes in Theories with Large Extra Dimensions: a Review
• Minimal Length Uncertainty Relation and Ultraviolet Regularisation
• Signatures in the Planck Regime
• Black hole and brane production in TeV gravity: A review
• Calculating Vacuum Energies in Renormalizable Quantum Field Theories: A New Approach to the Casimir Problem
• Casimir Effect on the Worldline
• Casimir Effect Between World-Branes in Heterotic M-Theory
• Duality and zero-point length of spacetime
• Casimir effect in de Sitter and Anti-de Sitter braneworlds
• Quantum Stabilization of Compactified AdS_5
• Casimir Energy and Radius Stabilization in Five and Six Dimensional Orbifolds
• Large radii and string unification
• Wave-Particle duality at the Planck scale: Freezing of neutrino oscillations
• Selected topics in Planck-scale physics
• Quantized bulk scalar fields in the Randall-Sundrum brane-model
• Quantum (In)Stability of a Brane-World AdS${}_5$ Universe at Nonzero Temperature
• The Casimir Effect on Background of Conformally Flat Brane--World Geometries
• A stable hierarchy from Casimir forces and the holographic interpretation
• Running Coupling with Minimal Length
• (De)Stabilization of an extra dimension due to a Casimir force
• Bulk versus boundary (gravitational Casimir) effects in quantum creation of inflationary brane-world Universe
• Brane Worlds and the Cosmic Coincidence Problem
• The Minimal Length and Large Extra Dimensions
• Casimir energy for de Sitter branes in bulk AdS(5)
• Suppressed Black Hole Production from Minimal Length
• Generalized Quantum Relativistic Kinematics: a Stability Point of View
• Casimir energy-momentum tensor for a brane in de Sitter spacetime
• The hypothesis of path integral duality II: corrections to quantum field theoretic results
• Matching the observational value of the cosmological constant
• Casimir energy of a non-uniform string
• Constraints on extra dimensions from cosmological and terrestrial measurements
• Casimir Effect on the Radius Stabilization of the Noncommutative Torus
• Primordial Inflation and Present-Day Cosmological Constant from Extra Dimensions
• Inflation in Multidimensional Quantum Cosmology

Cited by in corpus (47)

• Minimal Length Scale Scenarios for Quantum Gravity
• Black hole thermodynamics with generalized uncertainty principle
• Interpretation of Quantum Field Theories with a Minimal Length Scale
• Gauge Theories under Incorporation of a Generalized Uncertainty Principle
• Regularization of the Singular Inverse Square Potential in Quantum Mechanics with a Minimal length
• Statistical physics in deformed spaces with minimal length
• The Casimir Effect in Minimal Length Theories based on a Generalized Uncertainity Principle
• Singularities and the Finale of Black Hole Evaporation
• New agegraphic dark energy model with generalized uncertainty principle
• Entropy of the Randall-Sundrum brane world with the generalized uncertainty principle
• Hydrogen atom in momentum space with a minimal length
• Neutrino oscillations as a novel probe for a 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
• Local effects of the quantum vacuum in Lorentz-violating electrodynamics
• On the Minimal Length Uncertainty Relation and the Foundations of String Theory
• Casimir Effect confronts Cosmological Constant
• Vacuum Energy, the Cosmological Constant and Compact Extra Dimensions: Constraints from Casimir Effect Experiments
• Position and Momentum Uncertainties of the Normal and Inverted Harmonic Oscillators under the Minimal Length Uncertainty Relation
• Electroweak Theory with a Minimal Length
• Heuristic derivation of Casimir effect in minimal length theories
• Singular inverse square potential in coordinate space with a minimal length
• Regular black holes with sub-Planckian curvature
• Kratzer's molecular potential in quantum mechanics with a generalized uncertainty principle
• Casimir-Polder intermolecular forces in minimal length theories
• Boundaries and the Casimir effect in non-commutative space-time
• On the (2+1)-dimensional Dirac equation in a constant magnetic field with a minimal length uncertainty
• Influence of a Minimal Length on the Creation of Scalar Particles
• Path Integral for non-relativistic Generalized Uncertainty Principle corrected Hamiltonian
• Maximally Localized States in Quantum Mechanics with a Modified Commutation Relation to All Orders
• Modified dispersion relations and the response of the rotating Unruh-DeWitt detector
• Effect of Minimal lengths on Electron Magnetism
• Exact solutions of the (2+1) -dimensional Dirac oscillator under a magnetic field in the presence of a minimal length in the noncommutative phase-space
• Minimal spatio-temporal extent of events, neutrinos, and the cosmological constant problem
• Pseudoharmonic oscillator in quantum mechanics with a minimal length
• Generalized uncertainty principle and thermostatistics: a semiclassical approach
• Quantum Statistical Entropy and Minimal Length of 5D Ricci-flat Black String with Generalized Uncertainty Principle
• Dirac $\delta$-function potential in quasiposition representation of a minimal-length scenario
• On the stability of the dark energy based on generalized uncertainty principle
• A Maximum Force Perspective on Black Hole Thermodynamics, Quantum Pressure, and Near-Extremality
• The generalized uncertainty principle in the presence of extra dimensions
• Position and momentum uncertainties of a particle in a V-shaped potential under the minimal length uncertainty relation
• Casimir effect in polymer scalar field theory
• Transition Rate and the Photoelectric Effect in the Presence of a Minimal Length
• Particle in a cavity in one-dimensional bandlimited quantum mechanics
• Gravitational waveforms from periodic orbits around a novel regular black hole
• Casimir effect in deformed field
• Scalar Casimir effect for a conducting cylinder in a Lorentz violating background