Polymer and Fock representations for a Scalar field

Abstract

In loop quantum gravity, matter fields can have support only on the `polymer-like' excitations of quantum geometry, and their algebras of observables and Hilbert spaces of states can not refer to a classical, background geometry. Therefore, to adequately handle the matter sector, one has to address two issues already at the kinematic level. First, one has to construct the appropriate background independent operator algebras and Hilbert spaces. Second, to make contact with low energy physics, one has to relate this `polymer description' of matter fields to the standard Fock description in Minkowski space. While this task has been completed for gauge fields, important gaps remained in the treatment of scalar fields. The purpose of this letter is to fill these gaps.

13 pages, no figures

Cited by in corpus (81)

• Background Independent Quantum Gravity: A Status Report
• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• Fundamental Structure of Loop Quantum Gravity
• Loop quantum gravity: an outside view
• Spherically Symmetric Quantum Geometry: States and Basic Operators
• Spherically Symmetric Quantum Geometry: Hamiltonian Constraint
• Improved limit on quantum-spacetime modifications of Lorentz symmetry from observations of gamma-ray blazars
• Quantum resolution of black hole singularities
• Generalized uncertainty principles and localization in discrete space
• Extension of loop quantum gravity to $f(R)$ theories
• On (Cosmological) Singularity Avoidance in Loop Quantum Gravity
• The loop gravity string
• On effective loop quantum geometry of Schwarzschild interior
• Uniqueness of the Fock quantization of the Gowdy $T^3$ model
• Nonperturbative Loop Quantization of Scalar-Tensor Theories of Gravity
• Loop quantum $f(R)$ theories
• Cosmological singularity resolution from quantum gravity: the emergent-bouncing universe
• The Quantum Configuration Space of Loop Quantum Cosmology
• The LQG -- String: Loop Quantum Gravity Quantization of String Theory I. Flat Target Space
• Non-minimal couplings, quantum geometry and black hole entropy
• Effective constraints of loop quantum gravity
• High energy modifications of blackbody radiation and dimensional reduction
• Quantum Reduced Loop Gravity and the foundation of Loop Quantum Cosmology
• Polymer quantization of the free scalar field and its classical limit
• Low energy Lorentz violation from modified dispersion at high energies
• Background independent quantization and wave propagation
• Background independent quantizations: the scalar field I
• Quantization of the Jackiw-Teitelboim model
• Semiclassical states for quantum cosmology
• An embedding of loop quantum cosmology in (b, v) variables into a full theory context
• Background independent quantizations: the scalar field II
• Ultraviolet behavior in background independent quantum field theory
• Loop quantum gravity coupled to a scalar field
• Towards Loop Quantum Supergravity (LQSG) II. p-Form Sector
• Loop Quantum Brans-Dicke Theory
• Dynamics and entanglement in spherically symmetric quantum gravity
• Primordial polymer perturbations
• Dynamics of Scalar Field in Polymer-like Representation
• Quantum Hamiltonian for gravitational collapse
• Unimodular Loop Quantum Cosmology
• Polymer Quantization predicts radiation in inertial frames
• Band structure in the polymer quantization of the harmonic oscillator
• Embedding loop quantum cosmology without piecewise linearity
• Path Integral representation for Polymer Quantized Scalar Fields
• Polymer Quantum Dynamics of the Taub Universe
• A critical analysis of the cosmological implementation of Loop Quantum Gravity
• Polymer inflation
• Immirzi parameter without Immirzi ambiguity: Conformal loop quantization of scalar-tensor gravity
• Extension of Loop Quantum Gravity to Metric Theories beyond General Relativity
• Polymer quantization of CGHS model- I
• Exploring the diffeomorphism invariant Hilbert space of a scalar field
• Low energy Lorentz violation from high energy modified dispersion in inertial and circular motion
• Ashtekar-Barbero holonomy on the hyperboloid: Immirzi parameter as a Cut-off for Quantum Gravity
• Polymer quantization and Symmetries
• Loop quantum modified gravity and its cosmological application
• The Polymer representation for the scalar field: A Wigner functional approach
• Quantization of time and the big bang via scale-invariant loop gravity
• Quantum reduced loop gravity: extension to scalar field
• Response of a rotating detector coupled to a polymer quantized field
• Note on Canonical Quantization and Unitary Equivalence in Field Theory
• Polymer-Fourier quantization of the scalar field revisited
• Semiclassical cosmology with polymer matter
• Bounds on the Polymer Scale from Gamma Ray Bursts
• Natural Inflation from Polymer Quantization
• Polymer quantization and advanced gravitational wave detector
• Topologically inequivalent quantizations
• Matter in Loop Quantum Gravity
• Loop representation and r-Fock measures for $SU(N)$ gauge theories
• Casimir effect in polymer scalar field theory
• Localization and diffusion in polymer quantum field theory
• Frustration of resonant preheating by exotic kinetic terms
• Loop Quantum Vector-Tensor Gravity and Its Spherically Symmetric Model
• Expansion operators in spherically symmetric loop quantum gravity
• Spontaneous symmetry breaking in Loop Quantum Gravity
• A note on conformally compactified connection dynamics tailored for anti-de Sitter space
• Regularization of the cosmological sector of loop quantum gravity with bosonic matter and the related problems with general covariance of quantum corrections
• Quantum Groups and Polymer Quantum Mechanics
• Strong Equivalence Principle in Polymer Quantum Mechanics and deformed Heisenberg Algebra
• The Proca-field in Loop Quantum Gravity
• How is Lorentz Invariance encoded in the Hamiltonian?
• Abelian 2+1D Loop Quantum Gravity Coupled to a Scalar Field