Localization and diffusion in polymer quantum field theory
arXiv:1408.2959 · doi:10.1103/PhysRevD.90.104036
Abstract
Polymer quantization is a non-standard approach to quantizing a classical system inspired by background independent approaches to quantum gravity such as loop quantum gravity. When applied to field theory it introduces a characteristic polymer scale at the level of the fields classical configuration space. Compared with models with space-time discreteness or non-commutativity this is an alternative way in which a characteristic scale can be introduced in a field theoretic context. Motivated by this comparison we study here localization and diffusion properties associated with polymer field observables and dispersion relation in order to shed some light on the novel physical features introduced by polymer quantization. While localization processes seems to be only mildly affected by polymer effects, we find that polymer diffusion differs significantly from the "dimensional reduction" picture emerging in other Planck-scale models beyond local quantum field theory.
arXiv comment16 pages, 5 figures
References in corpus (37)
- Noncommutative Field Theory
- Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
- Nonstandard optics from quantum spacetime
- Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
- The Spin Foam Approach to Quantum Gravity
- Spectral Dimension of the Universe
- Quantum gravity corrections to neutrino propagation
- Tests of Lorentz invariance: a 2013 update
- Fractal Spacetime Structure in Asymptotically Safe Gravity
- Quantum gravity, shadow states, and quantum mechanics
- Fractal properties of quantum spacetime
- Quantum Mechanics of a Point Particle in 2+1 Dimensional Gravity
- De Sitter space as an arena for Doubly Special Relativity
- Fractal Structure of Loop Quantum Gravity
- Doubly Special Relativity and de Sitter space
- Complementarity of representations in quantum mechanics
- Polymer and Fock representations for a Scalar field
- Relation between polymer and Fock excitations
- Probing the quantum nature of spacetime by diffusion
- Background independent quantization and the uncertainty principle
- Spectral dimension as a probe of the ultraviolet continuum regime of causal dynamical triangulations
- Gravity on a multifractal
- Diffusion on -Minkowski space
- The propagator in polymer quantum field theory
- Quantum group symmetry and particle scattering in (2+1)-dimensional quantum gravity
- From dispersion relations to spectral dimension - and back again
- What is a particle?
- Topological field theory and the quantum double of SU(2)
- Anomalous dimension in semiclassical gravity
- Anatomy of a deformed symmetry: field quantization on curved momentum space
- Polymer state approximations of Schroedinger wave functions
- Planck-scale dimensional reduction without a preferred frame
- Background independent quantization and wave propagation
- Black hole entropy divergence and the uncertainty principle
- Ultraviolet behavior in background independent quantum field theory
- Kinematics of a relativistic particle with de Sitter momentum space
- Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity