On Noncommutative Geometric Regularisation

Abstract

Studies in string theory and in quantum gravity suggest the existence of a finite lower bound to the possible resolution of lengths which, quantum theoretically, takes the form of a minimal uncertainty in positions $\Delta x_0$. A finite minimal uncertainty in momenta $\Delta p_0$ has been motivated from the absence of plane waves on generic curved spaces. Both effects can be described as small noncommutative geometric features of space-time. In a path integral approach to the formulation of field theories on noncommutative geometries, we can now generally prove IR regularisation for the case of noncommutative geometries which imply minimal uncertainties $\Delta p_0$ in momenta.

LaTex, 9 pages

References in corpus (2)

• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Maximal Localisation in the Presence of Minimal Uncertainties in Positions and Momenta

Cited by in corpus (34)

• Minimal Length Scale Scenarios for Quantum Gravity
• Nonpointlike Particles in Harmonic Oscillators
• Modified theories of Gravity: Why, How and What?
• On Quantum Field Theory with Nonzero Minimal Uncertainties in Positions and Momenta
• Composite system in deformed space with minimal length
• Deformed Heisenberg algebra with minimal length and equivalence principle
• On the Space-Time Uncertainty Relations of Liouville Strings and D Branes
• Position and Momentum Uncertainties of the Normal and Inverted Harmonic Oscillators under the Minimal Length Uncertainty Relation
• Free particle wavefunction in light of the minimum-length deformed quantum mechanics and some of its phenomenological implications
• Singular inverse square potential in coordinate space with a minimal length
• Hubble tension bounds the GUP and EUP parameters
• Quantum-Corrected Black Hole Thermodynamics in Extra Dimensions
• Corrections to the black body radiation due to minimum-length deformed quantum mechanics
• Kratzer's molecular potential in quantum mechanics with a generalized uncertainty principle
• Minimal Scales from an Extended Hilbert Space
• Natural Cutoffs via Compact Symplectic Manifolds
• Deformed Heisenberg algebra and minimal length
• New higher-order generalized uncertainty principle: Applications
• On Nonlocality, Lattices and Internal Symmetries
• Constraining the generalized uncertainty principle with neutron interferometry
• Extending general covariance: Moyal-type noncommutative manifolds
• Late time cosmic acceleration from natural infrared cutoff?
• Minimum-length deformed quantization of a free field on de Sitter background and corrections to the inflaton perturbations
• Relation of deformed nonlinear algebras with linear ones
• Corrections to the Emergent Canonical Commutation Relations Arising in the Statistical Mechanics of Matrix Models
• Visible Energy Alternative to Dark Energy
• Position and momentum uncertainties of a particle in a V-shaped potential under the minimal length uncertainty relation
• Some consequences of GUP induced ultraviolet wavevector cutoff in one-dimensional Quantum Mechanics
• Minimal length estimation on the basis of studies of the Sun-Earth-Moon system in deformed space
• Generalized uncertainty principle and burning stars
• Kinematics and uncertainty relations of a quantum test particle in a curved space-time
• Three Short Distance Structures from Quantum Algebras
• Hilbert space representation of maximal length and minimal momentum uncertainties
• Exact continuity equation in a space with minimal length