Galileo Symmetries in Polymer Particle Representation

Abstract

To illustrate the conceptual problems for the low-energy symmetries in the continuum of spacetime emerging from the discrete quantum geometry, Galileo symmetries are investigated in the polymer particle representation of a non-relativistic particle as a simple toy model. The complete Galileo transformations (translation, rotation and Galileo boost) are naturally defined in the polymer particle Hilbert space and Galileo symmetries are recovered with highly suppressed deviations in the low-energy regime from the underlying polymer particle description.

20 pages; version to appear in Class. Quant. Grav

References in corpus (8)

• Quantum gravity, shadow states, and quantum mechanics
• Relation between polymer and Fock excitations
• Fock representations from U(1) holonomy algebras
• Photons from quantized electric flux representations
• Gravitons from a loop representation of linearised gravity
• Minkowski vacuum in background independent quantum gravity
• A proposal for analyzing the classical limit of kinematic loop gravity
• Invariance properties of induced Fock measures for U(1) holonomies

Cited by in corpus (11)

• Polymer Quantum Mechanics and its Continuum Limit
• Propagators in Polymer Quantum Mechanics
• Polymer Bose--Einstein Condensates
• Statistical Thermodynamics of Polymer Quantum Systems
• Tunneling in Polymer Quantization and the Quantum Zeno Effect
• Polymer quantization and Symmetries
• Polymer quantum effects on compact stars models
• The symplectic group in Polymer Quantum Mechanics
• Relativistic Planck-scale polymer
• Strong Equivalence Principle in Polymer Quantum Mechanics and deformed Heisenberg Algebra
• Quantum Groups and Polymer Quantum Mechanics