Polymer Parametrised Field Theory

Abstract

Free scalar field theory on 2 dimensional flat spacetime, cast in diffeomorphism invariant guise by treating the inertial coordinates of the spacetime as dynamical variables, is quantized using LQG type `polymer' representations for the matter field and the inertial variables. The quantum constraints are solved via group averaging techniques and, analogous to the case of spatial geometry in LQG, the smooth (flat) spacetime geometry is replaced by a discrete quantum structure. An overcomplete set of Dirac observables, consisting of (a) (exponentials of) the standard free scalar field creation- annihilation modes and (b) canonical transformations corresponding to conformal isometries, are represented as operators on the physical Hilbert space. None of these constructions suffer from any of the `triangulation' dependent choices which arise in treatments of LQG. In contrast to the standard Fock quantization, the non- Fock nature of the representation ensures that the algebra of conformal isometries as well as that of spacetime diffeomorphisms are represented in an anomaly free manner. Semiclassical states can be analysed at the gauge invariant level. It is shown that `physical weaves' necessarily underly such states and that such states display semiclassicality with respect to, at most, a countable subset of the (uncountably large) set of observables of type (a). The model thus offers a fertile testing ground for proposed definitions of quantum dynamics as well as semiclassical states in LQG.

44 pages, no figures

References in corpus (23)

• Background Independent Quantum Gravity: A Status Report
• Discreteness of area and volume in quantum gravity
• Quantum Geometry and Black Hole Entropy
• Quantum Theory of Gravity I: Area Operators
• Loop Quantum Gravity
• Black Hole Entropy from Loop Quantum Gravity
• Spin Foam Models for Quantum Gravity
• Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
• Weaving a classical geometry with quantum threads
• Uniqueness of diffeomorphism invariant states on holonomy-flux algebras
• Quantum gravity, shadow states, and quantum mechanics
• Lectures on Loop Quantum Gravity
• Graviton propagator from background-independent quantum gravity
• Gauge Field Theory Coherent States (GCS) : I. General Properties
• Algebraic Quantum Gravity (AQG) I. Conceptual Setup
• Coherent States for Canonical Quantum General Relativity and the Infinite Tensor Product Extension
• On the Generality of Refined Algebraic Quantization
• Gauge Field Theory Coherent States (GCS) : IV. Infinite Tensor Product and Thermodynamical Limit
• Quantum Theory of Geometry III: Non-commutativity of Riemannian Structures
• Quantum Fields at Any Time
• A proposal for analyzing the classical limit of kinematic loop gravity
• The graviton vacuum as a distributional state in kinematic Loop Quantum Gravity
• Polymer quantization of CGHS model- I

Cited by in corpus (19)

• From the discrete to the continuous - towards a cylindrically consistent dynamics
• Time evolution as refining, coarse graining and entangling
• Polymer quantization of the free scalar field and its classical limit
• Gravitational effects in macroscopic quantum systems: a first-principles analysis
• The Hamiltonian constraint in Polymer Parametrized Field Theory
• Diffeomorphism symmetry in quantum gravity models
• Band structure in the polymer quantization of the harmonic oscillator
• Propagation in Polymer Parameterised Field Theory
• Lessons for Loop Quantum Gravity from Parametrised Field Theory
• Loop Quantum Gravity and Cosmology: A dynamical introduction
• Towards general relativity through parametrized theories
• Quantum geometry with a nondegenerate vacuum: a toy model
• Matter in Loop Quantum Gravity
• Hamiltonian dynamics of the parametrized electromagnetic field
• Asymptotic Flatness and Quantum Geometry
• Equivalence of the self-dual and Nambu-Goto strings
• Geometrical Quantum Time in the $U(1{)}^3$ Model of Euclidean Quantum Gravity
• Quantum gravity effects on space-time
• Functional evolution of scalar fields in bounded one-dimensional regions