Semiclassical Limit of New Path Integral Formulation from Reduced Phase Space Loop Quantum Gravity

Abstract

Recently, a new path integral formulation of Loop Quantum Gravity (LQG) has been derived in arXiv:1910.03763 from the reduced phase space formulation of the canonical LQG. This paper focuses on the semiclassical analysis of this path integral formulation. We show that dominant contributions of the path integral come from solutions of semiclassical equations of motion (EOMs), which reduces to Hamilton's equations of holonomies and fluxes $h(e),p^a(e)$ in the reduced phase space ${\mathcal{P}}_{\gamma }$ of the cubic lattice $\gamma$: $\dot{h}(e)=\{h(e),\mathbf{H}\}$, ${\dot{p}}^a(e)=\{p^a(e),\mathbf{H}\}$, where $\mathbf{H}$ is the discrete physical Hamiltonian. The semiclassical dynamics from the path integral becomes an initial value problem of Hamiltonian time evolution in ${\mathcal{P}}_{\gamma }$. Moreover when we take the continuum limit of the lattice $\gamma$, these Hamilton's equations reproduce correctly classical reduced phase space EOMs of gravity coupled to dust fields in the continuum, as far as initial and final states are semiclassical. Our result proves that the new path integral formulation has the correct semiclassical limit, and indicates that the reduced phase space quantization in LQG is semiclassically consistent. Based on these results, we compare this path integral formulation and the spin foam formulation, and show that this formulation has several advantages including the finiteness, the relation with canonical LQG, and being free of cosine and flatness problems.

arXiv comment25+3 pages, no figure. ILQGS talk: http://relativity.phys.lsu.edu/ilqgs/han041420.mp4. Mathematica files can be downloaded from https://github.com/LQG-Florida-Atlantic-University/Classical-EOM

References in corpus (65)

• The Spin Foam Approach to Quantum Gravity
• Dust as a Standard of Space and Time in Canonical Quantum Gravity
• QSD V : Quantum Gravity as the Natural Regulator of Matter Quantum Field Theories
• Partial observables
• Partial and Complete Observables for Hamiltonian Constrained Systems
• Lorentzian spin foam amplitudes: graphical calculus and asymptotics
• Asymptotic analysis of the EPRL four-simplex amplitude
• On the semiclassical limit of 4d spin foam models
• Gauge Field Theory Coherent States (GCS) : I. General Properties
• Gauge Field Theory Coherent States (GCS) : II. Peakedness Properties
• Three dimensional loop quantum gravity: physical scalar product and spin foam models
• Algebraic Quantum Gravity (AQG) I. Conceptual Setup
• Algebraic Quantum Gravity (AQG) IV. Reduced Phase Space Quantisation of Loop Quantum Gravity
• Scalar Material Reference Systems and Loop Quantum Gravity
• Reduced Phase Space Quantization and Dirac Observables
• Gauge Field Theory Coherent States (GCS) : III. Ehrenfest Theorems
• LQG propagator from the new spin foams
• Bouncing cosmologies from quantum gravity condensates
• Numerical evidence for a phase transition in 4d spin foam quantum gravity
• Spin foam models for quantum gravity from lattice path integrals
• 4-dimensional Spin-foam Model with Quantum Lorentz Group
• Quantum deformation of two four-dimensional spin foam models
• Casting Loop Quantum Cosmology in the Spin Foam Paradigm
• Towards the QFT on Curved Spacetime Limit of QGR. I: A General Scheme
• Self-Energy of the Lorentzian EPRL-FK Spin Foam Model of Quantum Gravity
• Manifestly Gauge-Invariant General Relativistic Perturbation Theory: I. Foundations
• SL(2,C) Chern-Simons Theory, a non-Planar Graph Operator, and 4D Loop Quantum Gravity with a Cosmological Constant: Semiclassical Geometry
• Lorentzian spinfoam propagator
• Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Lorentzian Theory
• Numerical study of the Lorentzian Engle-Pereira-Rovelli-Livine spin foam amplitude
• Algebraic Quantum Gravity (AQG) III. Semiclassical Perturbation Theory
• Manifestly Gauge-Invariant General Relativistic Perturbation Theory: II. FRW Background and First Order
• Cosmological Constant in LQG Vertex Amplitude
• Cosmological perturbations from full quantum gravity
• Holonomy spin foam models: Asymptotic geometry of the partition function
• Linking covariant and canonical LQG: new solutions to the Euclidean Scalar Constraint
• Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Euclidean Theory
• New scalar constraint operator for loop quantum gravity
• Numerical methods for EPRL spin foam transition amplitudes and Lorentzian recoupling theory
• Effective Dynamics from Coherent State Path Integral of Full Loop Quantum Gravity
• Spinfoams in the holomorphic representation
• On Spinfoam Models in Large Spin Regime
• Black Holes as Quantum Gravity Condensates
• Numerical analysis of spin foam dynamics and the flatness problem
• Asymptotic analysis of spin foam amplitude with timelike triangles
• Linking covariant and canonical LQG II: Spin foam projector
• Einstein Equation from Covariant Loop Quantum Gravity in Semiclassical Continuum Limit
• The Feynman propagator for spin foam quantum gravity
• Local spinfoam expansion in loop quantum cosmology
• Towards a Cosmological subsector of Spin Foam Quantum Gravity
• Emergence of gravity from spinfoams
• On the Relation between Operator Constraint --, Master Constraint --, Reduced Phase Space --, and Path Integral Quantisation
• Covariant Loop Quantum Gravity, Low Energy Perturbation Theory, and Einstein Gravity with High Curvature UV Corrections
• Quantum Spacetime on a Quantum Simulator
• Searching for classical geometries in spin foam amplitudes: a numerical method
• Emergent 4-dimensional linearized gravity from spin foam model
• Infrared divergences in the EPRL-FK Spin Foam model
• Bulk amplitude and degree of divergence in 4d spin foams
• Efficient Simulation of Loop Quantum Gravity -- A Scalable Linear-Optical Approach
• On the Relation between Rigging Inner Product and Master Constraint Direct Integral Decomposition
• Spin-foam model for gravity coupled to massless scalar field
• Holonomy-flux spinfoam amplitude
• Canonical path integral measures for Holst and Plebanski gravity. I. Reduced Phase Space Derivation
• Canonical Path-Integral Measures for Holst and Plebanski Gravity. II. Gauge Invariance and Physical Inner Product
• Spin foam propagator: A new perspective to include a cosmological constant

Cited by in corpus (16)

• Improved Effective Dynamics of Loop-Quantum-Gravity Black Hole and Nariai Limit
• Spherical symmetric gravitational collapse of a dust cloud: polymerized dynamics in reduced phase space
• Improved ($\bar{\mu }$-Scheme) Effective Dynamics of Full Loop Quantum Gravity
• Phenomenological implications of modified loop cosmologies: an overview
• First-Order Quantum Correction in Coherent State Expectation Value of Loop-Quantum-Gravity Hamiltonian
• Loop Quantum Gravity on Dynamical Lattice and Improved Cosmological Effective Dynamics with Inflaton
• Manifestly Gauge-Invariant Cosmological Perturbation Theory from Full Loop Quantum Gravity
• Superposition type coherent states in all dimensional loop quantum gravity
• Twisted geometry coherent states in all dimensional loop quantum gravity: I. Construction and Peakedness properties
• The effective dynamics of weak coupling loop quantum gravity
• Spinfoams: Foundations
• Modifications to Gravitational Wave Equation from Canonical Quantum Gravity
• Twisted geometry coherent states in all dimensional loop quantum gravity: II. Ehrenfest Property
• Toward matter dynamics in spin foam quantum gravity
• Coherent states for fractional powers of the harmonic oscillator Hamiltonian
• The Semiclassical limit of $SU(3)$ Gauge Field Coherent States: Peakedness and Overlap Functions