Path Integrals and the WKB approximation in Loop Quantum Cosmology

Abstract

We follow the Feynman procedure to obtain a path integral formulation of loop quantum cosmology starting from the Hilbert space framework. Quantum geometry effects modify the weight associated with each path so that the effective measure on the space of paths is different from that used in the Wheeler-DeWitt theory. These differences introduce some conceptual subtleties in arriving at the WKB approximation. But the approximation is well defined and provides intuition for the differences between loop quantum cosmology and the Wheeler-DeWitt theory from a path integral perspective.

21 pages, 4 figures

References in corpus (19)

• Quantum Nature of the Big Bang: Improved dynamics
• Quantum Nature of the Big Bang
• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• Robustness of key features of loop quantum cosmology
• Loop quantum cosmology of k=1 FRW models
• Uniqueness of diffeomorphism invariant states on holonomy-flux algebras
• Loop quantum cosmology of Bianchi I models
• Corrections to the Friedmann Equations from LQG for a Universe with a Free Scalar Field
• Loop Quantum Cosmology: An Overview
• Representations of the Weyl Algebra in Quantum Geometry
• Loop quantum cosmology of Bianchi type IX models
• Closed FRW model in Loop Quantum Cosmology
• Anti-deSitter universe dynamics in LQC
• Loop quantum cosmology of Bianchi type II models
• Casting Loop Quantum Cosmology in the Spin Foam Paradigm
• Loop Quantum Cosmology and Spin Foams
• Path Integrals and Instantons in Quantum Gravity
• The flat FRW model in LQC: the self-adjointness
• Vertex Expansion for the Bianchi I model

Cited by in corpus (50)

• Loop Quantum Cosmology: A Status Report
• The Spin Foam Approach to Quantum Gravity
• Loop quantum cosmology of Bianchi I models
• The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations
• An Extension of the Quantum Theory of Cosmological Perturbations to the Planck Era
• Loop quantum cosmology: From pre-inflationary dynamics to observations
• Coherent semiclassical states for loop quantum cosmology
• On effective loop quantum geometry of Schwarzschild interior
• On the Semiclassical Limit of Loop Quantum Cosmology
• Many-nodes/many-links spinfoam: the homogeneous and isotropic case
• The Vacuum State of Primordial Fluctuations in Hybrid Loop Quantum Cosmology
• Regge gravity from spinfoams
• Spherical symmetric gravitational collapse of a dust cloud: polymerized dynamics in reduced phase space
• Propagators in Polymer Quantum Mechanics
• Loop Quantum Cosmology: A brief review
• Consistent probabilities in loop quantum cosmology
• Loop quantum Brans-Dicke cosmology
• Instability of an emergent universe
• Coherent State Functional Integral in Loop Quantum Cosmology: Alternative Dynamics
• Polymer quantization and the saddle point approximation of partition functions
• Path Integrals and Alternative Effective Dynamics in Loop Quantum Cosmology
• Higher dimensional Loop Quantum Cosmology
• Lorentz Symmetry in QFT on Quantum Bianchi I Space-Time
• Loop Quantum Cosmology
• The no-boundary wave function for loop quantum cosmology
• The Lorentzian proper vertex amplitude: Classical analysis and quantum derivation
• Coherent State Functional Integrals in Quantum Cosmology
• Path Integral representation for Polymer Quantized Scalar Fields
• Symmetry Reduced Loop Quantum Gravity: A Bird's Eye View
• Diffeomorphism invariant cosmological sector in loop quantum gravity
• The consistent histories approach to loop quantum cosmology
• Loop quantum modified gravity and its cosmological application
• Dynamical eigenfunctions and critical density in loop quantum cosmology
• Anomaly freedom of the vector modes with holonomy corrections in perturbative Euclidean loop quantum gravity
• The time-dependent mass of cosmological perturbations in loop quantum cosmology: Dapor-Liegener regularization
• Bounds on the Polymer Scale from Gamma Ray Bursts
• Instanton solutions on the polymer harmonic oscillator
• Gravitational waves with generalized holonomy corrections
• Loop quantum cosmology in 2+1 dimension
• Loop quantum cosmological dynamics of scalar-tensor theory in the Jordan frame
• Path Integral of Bianchi I models in Loop Quantum Cosmology
• Testing general covariance in effective models motivated by Loop Quantum Gravity
• Towards a Hartle-Hawking state for loop quantum gravity
• Cosmological dynamics in spin-foam loop quantum cosmology: challenges and prospects
• The Nature and Origin of Time-asymmetric Spacetime Structures
• Effective Theories of Quantum Cosmology
• A Twisted ${\mathcal{C}}^{\star }$-algebra formulation of Quantum Cosmology with application to the Bianchi I model
• Quantisation ambiguities and the effective dynamics of scalar-tensor theories in loop quantum cosmology
• Space-like Singularities of General Relativity: A Phantom menace?
• Unitary evolution and cosmic acceleration in Loop Quantum Cosmology