Polymer state approximations of Schroedinger wave functions

Abstract

It is shown how states of a quantum mechanical particle in the Schroedinger representation can be approximated by states in the so-called polymer representation. The result may shed some light on the semiclassical limit of loop quantum gravity.

11 pages, 1 figure, Conclusions section added

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• Polymer Quantum Cosmology: Lifting quantization ambiguities using a $SL(2,\mathbb{R})$ conformal symmetry
• Natural Cutoffs via Compact Symplectic Manifolds
• Semiclassical states for quantum cosmology
• Primordial polymer perturbations
• Thermostatistics of the Polymeric Ideal Gas
• Polymer Quantum Dynamics of the Taub Universe
• Bounds on quantum gravity parameter from the $SU(2)$ NJL effective model of QCD
• Statistical Thermodynamics of Polymer Quantum Systems
• Polymer inflation
• Tunneling in Polymer Quantization and the Quantum Zeno Effect
• Polymer quantization versus the Snyder noncommutative space
• Noncommutative spaces and covariant formulation of statistical mechanics
• Violation of the Holographic Principle in the Loop Quantum Gravity
• Semiclassical cosmology with polymer matter
• Entropy and entanglement in polymer quantization
• Relativistic Planck-scale polymer
• The polymer quantization in LQG: massless scalar field
• Localization and diffusion in polymer quantum field theory
• Frustration of resonant preheating by exotic kinetic terms
• Superfluids in Polymer Quantum Mechanics
• Dimensional Phenomenology in Polymeric Quantization Framework