n-dimensional non-commutative GUP quantization and application to the Bianchi I model

Abstract

We analyse a n-dimensional Generalized Uncertainty Principle (GUP) quantization framework, characterized by a non-commutative nature of the configurational variables. First, we identify a set of states which are maximally localized only along a single direction, at the expense of being less localized in all the other ones. Subsequently, in order to recover information about localization on the whole configuration space, we use the only state of the theory which exhibits maximal localization simultaneously in every direction to construct a satisfactory quasi-position representation, by virtue of a suitable translational operator. The resultant quantum framework is then applied to model the dynamics of the Bianchi I cosmology. The corresponding Wheeler-DeWitt equation is reduced to Schrödinger dynamics for the two anisotropy degrees of freedom, using a WKB representation for the volume-like variable of the Universe, in accordance with the Vilenkin scenario. The main result of our cosmological implementation of the constructed quantum theory demonstrates how the dynamics of a wave packet peaked at some point in the configuration space represented in the quasi-position variables, favours as the most probable configuration exactly the initial one for a relatively long time, if compared with the ordinary quantum theory. This preference arises from the distinct behavioral dynamics exhibited by wave packets in the two quantum theories.

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References in corpus (24)

• The Dynamics of General Relativity
• Minimal Length Scale Scenarios for Quantum Gravity
• Loop quantum cosmology of Bianchi I models
• 30 years in: Quo vadis generalized uncertainty principle?
• About maximally localized states in quantum mechanics
• On the Covariance of the Mixmaster Chaoticity
• Extended GUP formulation and the role of momentum cut-off
• On the quasi-position representation in theories with a minimal length
• An Overview on the Nature of the Bounce in LQC and PQM
• Inhomogeneous Quantum Mixmaster: from Classical toward Quantum Mechanics
• Comparison of the Semiclassical and Quantum Dynamics of the Bianchi I Cosmology in the Polymer and GUP Extended Paradigms
• Non-Unitarity Problem in Quantum Gravity Corrections to Quantum Field Theory with Born-Oppenheimer Approximation
• Quantum gravity corrections to the matter dynamics in the presence of a reference fluid
• QFT in Curved Spacetime from Quantum Gravity: proper WKB decomposition of the gravitational component
• Unveiling Phase Space Modifications: A Clash of Modified Gravity and the Generalized Uncertainty Principle
• Dynamics of quantum anisotropies in a Taub Universe in the WKB approximation
• Constraining Snyder and GUP models with low-mass stars
• Probabilistic interpretation of the wave function for the Bianchi I model
• Semiclassical suppression of weak anisotropies of a generic Universe
• Semiclassical and quantum features of the Bianchi I cosmology in the polymer representation
• Quantum dynamics of the corner of the Bianchi IX model in WKB approximation
• Loop Quantum Cosmology of non-diagonal Bianchi models
• Is the diagonal case a general picture for Loop Quantum Cosmology?
• The role of spatial curvature in constraining the Universe anisotropies across a Big Bounce

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• Szekeres Universes with GUP corrections
• Bouncing Bianchi Models with Deformed Commutation Relations
• Unitary equivalence in Generalized Uncertainty Principle theories
• Mixmaster chaos in a quantum scenario:a Deformed Algebra approach
• An algebraic approach to gravitational quantum mechanics