Generalized Uncertainty Principle and Quantum Electrodynamics

Abstract

In the present work the role that a generalized uncertainty principle could play in the quantization of the electromagnetic field is analyzed. It will be shown that we may speak of a Fock space, a result that implies that the concept of photon is properly defined. Nevertheless, in this new context the creation and annihilation operators become a function of the new term that modifies the Heisenberg algebra, and hence the Hamiltonian is not anymore diagonal in the occupation number representation. Additionally, we show the changes that the energy expectation value suffers as result of the presence of an extra term in the uncertainty principle. The existence of a deformed dispersion relation is also proved.

Acceptted in General Relativity and Gravitation

References in corpus (14)

• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Quantum Field Theory on Noncommutative Spaces
• Potential Sensitivity of Gamma-Ray Burster Observations to Wave Dispersion in Vacuo
• Nonstandard optics from quantum spacetime
• Quantum Groups, Gravity, and the Generalized Uncertainty Principle
• Quantum gravity corrections to neutrino propagation
• Classical and Quantum Mechanics of Free \k Relativistic Systems
• Minimal Length Uncertainty Relation and Ultraviolet Regularisation
• An interferometric gravitational wave detector as a quantum-gravity apparatus
• Astrophysical limits on quantum gravity motivated birefringence
• New Observational Bounds to Quantum Gravity Signals
• Observational Limits on Quantum Geometry Effects
• Space-time quantum solves three experimental paradoxes
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Cited by in corpus (16)

• Minimal Length Scale Scenarios for Quantum Gravity
• Some Aspects of Minimal Length Quantum Mechanics
• Quantum Mechanics and the Generalized Uncertainty Principle
• Gravitational Uncertainty and Black Hole Remnants
• Minimal Length and Bouncing Particle Spectrum
• Some Aspects of Planck Scale Quantum Optics
• Minimal Length and Generalized Dirac Equation
• Comparing two approaches to Hawking radiation of Schwarzschild-de Sitter black holes
• On the (2+1)-dimensional Dirac equation in a constant magnetic field with a minimal length uncertainty
• Primordial Power Spectra of Cosmological Fluctuations with Generalized Uncertainty Principle and Maximum Length Quantum Mechanics
• Wave Packets Propagation in Quantum Gravity
• Deformed Hamilton-Jacobi Method in Covariant Quantum Gravity Effective Models
• Lorentz invariant nonzero minimal uncertainty in position and inhomogeneity of space at the Planck scale
• Theory of a many-boson system with deformed Heisenberg algebra
• Homogeneous Field and WKB Approximation In Deformed Quantum Mechanics with Minimal Length
• Towards an Entropic Geometrodynamics of Quantum Particles: Mouths of Casimir Wormholes as Planckeons