Deformation of Second and Third Quantization

Abstract

In this paper, we will deform the second and third quantized theories by deforming the canonical commutation relations in such a way that they become consistent with the generalized uncertainty principle. Thus, we will first deform the second quantized commutator and obtain a deformed version of the Wheeler-DeWitt equation. Then we will further deform the third quantized theory by deforming the third quantized canonical commutation relation. This way we will obtain a deformed version of the third quantized theory for the multiverse.

10 pages, 0 figures, accepted for publication in Int. J. Mod. Phys. A

References in corpus (43)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Discovery of a Supernova Explosion at Half the Age of the Universe and its Cosmological Implications
• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Cosmological Results from High-z Supernovae
• Quantum gravity and minimum length
• A Generalized Uncertainty Principle in Quantum Gravity
• Generalized Uncertainty Principle in Quantum Gravity from Micro-Black Hole Gedanken Experiment
• Universality of Quantum Gravity Corrections
• Distributions of flux vacua
• The algebraic structure of the generalized uncertainty principle
• Quantum Groups, Gravity, and the Generalized Uncertainty Principle
• Nonpointlike Particles in Harmonic Oscillators
• Minimal Length Uncertainty Relation and Hydrogen Atom
• Exact Solution of the Harmonic Oscillator in Arbitrary Dimensions with Minimal Length Uncertainty Relations
• The Effect of the Minimal Length Uncertainty Relation on the Density of States and the Cosmological Constant Problem
• Counting Flux Vacua
• Brane New World
• Short Distance vs. Long Distance Physics: The Classical Limit of the Minimal Length Uncertainty Relation
• Mode Generating Mechanism in Inflation with Cutoff
• The Generalized Uncertainty Principle in (A)dS Space and the Modification of Hawking Temperature from the Minimal Length
• Natural extension of the Generalised Uncertainty Principle
• A Preliminary Indication of Evolution of Type Ia Supernovae from their Risetimes
• Some Aspects of Minimal Length Quantum Mechanics
• Gauge Theories under Incorporation of a Generalized Uncertainty Principle
• Minimum Length Cutoff in Inflation and Uniqueness of the Action
• Some Aspects of Planck Scale Quantum Optics
• A class of GUP solutions in deformed quantum mechanics
• How many universes are in the multiverse?
• Generalized uncertainty principles and quantum field theory
• 'Tilting' the Universe with the Landscape Multiverse: The 'Dark' Flow
• Unitary relation between a harmonic oscillator of time-dependent frequency and a simple harmonic oscillator with and without an inverse-square potential
• Geometric Phase, Hannay's Angle, and an Exact Action Variable
• Electroweak Theory with a Minimal Length
• The minimum length problem of loop quantum cosmology
• Deformation of the Wheeler-DeWitt Equation
• Super-Group Field Cosmology
• Some Aspects of Virtual Black Holes
• Multiverse in the Third Quantized Horava-Lifshits Theory of Gravity
• Third Quantization of Kaluza-Klein Cosmology and Compactification
• Third quantization of $f(R)$-type gravity
• Generalized Quantization Principle in Canonical Quantum Gravity and Application to Quantum Cosmology
• Fourth Quantization

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• Quantum Cosmology with Dynamical Vacuum in a Minimal-Length Scenario
• Super-group field cosmology in Batalin-Vilkovisky formulation
• Scalar field inflation driven by a modification of the Heisenberg algebra
• Virtual Black Holes in a Third Quantized Formalism
• Lorentzian Vacuum Transitions with a Generalized Uncertainty Principle