Spinfoams in the holomorphic representation

Abstract

We study a holomorphic representation for spinfoams. The representation is obtained via the Ashtekar-Lewandowski-Marolf-Mourão-Thiemann coherent state transform. We derive the expression of the 4d spinfoam vertex for Euclidean and for Lorentzian gravity in the holomorphic representation. The advantage of this representation rests on the fact that the variables used have a clear interpretation in terms of a classical intrinsic and extrinsic geometry of space. We show how the peakedness on the extrinsic geometry selects a single exponential of the Regge action in the semiclassical large-scale asymptotics of the spinfoam vertex.

10 pages, 1 figure, published version

References in corpus (52)

• Background Independent Quantum Gravity: A Status Report
• LQG vertex with finite Immirzi parameter
• Spin Foam Models for Quantum Gravity
• A new spinfoam vertex for quantum gravity
• ``Sum over Surfaces'' form of Loop Quantum Gravity
• A New Spin Foam Model for 4d Gravity
• Twisted geometries: A geometric parametrisation of SU(2) phase space
• 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
• Graviton propagator from background-independent quantum gravity
• Gauge Field Theory Coherent States (GCS) : I. General Properties
• Gauge Field Theory Coherent States (GCS) : II. Peakedness Properties
• Group field theory with non-commutative metric variables
• A "general boundary" formulation for quantum mechanics and quantum gravity
• Towards Spinfoam Cosmology
• Coherent States for Canonical Quantum General Relativity and the Infinite Tensor Product Extension
• The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex
• Group field theory renormalization - the 3d case: power counting of divergences
• Gauge Field Theory Coherent States (GCS) : III. Ehrenfest Theorems
• Gauge Field Theory Coherent States (GCS) : IV. Infinite Tensor Product and Thermodynamical Limit
• Spin-Foams for All Loop Quantum Gravity
• LQG propagator from the new spin foams
• Complexifier Coherent States for Quantum General Relativity
• A spin foam model without bubble divergences
• Scaling behaviour of three-dimensional group field theory
• Linearized Group Field Theory and Power Counting Theorems
• The length operator in Loop Quantum Gravity
• Coherent spin-networks
• Quantum geometry from phase space reduction
• Geometric quantization and the generalized Segal-Bargmann transform for Lie groups of compact type
• Particle scattering in loop quantum gravity
• Bubble divergences from cellular cohomology
• The complete LQG propagator: II. Asymptotic behavior of the vertex
• Lorentzian LQG vertex amplitude
• Projected Spin Networks for Lorentz connection: Linking Spin Foams and Loop Gravity
• Self-energy and vertex radiative corrections in LQG
• Holomorphic Factorization for a Quantum Tetrahedron
• Path integral representation of spin foam models of 4d gravity
• Face amplitude of spinfoam quantum gravity
• Gauge-invariant coherent states for Loop Quantum Gravity I: Abelian gauge groups
• Regularization and finiteness of the Lorentzian LQG vertices
• Gauge-invariant coherent states for Loop Quantum Gravity II: Non-abelian gauge groups
• From lattice BF gauge theory to area-angle Regge calculus
• LQG propagator: III. The new vertex
• Asymptotic analysis of the Ponzano-Regge model for handlebodies
• Semiclassical regime of Regge calculus and spin foams
• Numerical indications on the semiclassical limit of the flipped vertex
• Asymptotics of LQG fusion coefficients
• Encoding simplicial quantum geometry in group field theories
• Intertwiner dynamics in the flipped vertex
• Evaluation of new spin foam vertex amplitudes

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• Cosmological constant in spinfoam cosmology
• Operator Spin Foam Models
• Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Euclidean Theory
• A new look at loop quantum gravity
• Spinfoam fermions
• A proposed proper EPRL vertex amplitude
• Many-nodes/many-links spinfoam: the homogeneous and isotropic case
• Path Integral Representation of Lorentzian Spinfoam Model, Asymptotics, and Simplicial Geometries
• Regge gravity from spinfoams
• Simple model for quantum general relativity from loop quantum gravity
• Towards a Cosmological subsector of Spin Foam Quantum Gravity
• Emergence of gravity from spinfoams
• Semiclassical Limit of New Path Integral Formulation from Reduced Phase Space Loop Quantum Gravity
• Loop expansion and the bosonic representation of loop quantum gravity
• A Homogeneous Model of Spinfoam Cosmology
• Numerical computations of next-to-leading order corrections in spinfoam large-$j$ asymptotics
• Emergent 4-dimensional linearized gravity from spin foam model
• Learning about Quantum Gravity with a Couple of Nodes
• Feynman diagrammatic approach to spin foams
• The Plebanski sectors of the EPRL vertex
• Coherent states for FLRW space-times in loop quantum gravity
• Anisotropic Spinfoam Cosmology
• Spinfoam Fermions: PCT Symmetry, Dirac Determinant, and Correlation Functions
• Holonomy-flux spinfoam amplitude
• Towards a Loop Quantum Gravity and Yang-Mills Unification
• Spin foam amplitude of the black-to-white hole transition
• Searching for Coherent States: From Origins to Quantum Gravity
• Semi-Classical Holomorphic Transition Amplitudes in Covariant Loop Quantum Gravity
• First-order quantum-gravitational correction to Friedmannian cosmology from covariant, holomorphic spinfoam cosmology
• The relation between Geometry and Matter in classical and quantum Gravity and Cosmology