Coherent 3j-symbol representation for the loop quantum gravity intertwiner space

Abstract

We introduce a new technique for dealing with the matrix elements of the Hamiltonian operator in loop quantum gravity, based on the use of intertwiners projected on coherent states of angular momentum. We give explicit expressions for the projections of intertwiners on the spin coherent states in terms of complex numbers describing the unit vectors which label the coherent states. Operators such as the Hamiltonian can then be reformulated as differential operators acting on polynomials of these complex numbers. This makes it possible to describe the action of the Hamiltonian geometrically, in terms of the unit vectors originating from the angular momentum coherent states, and opens up a way towards investigating the semiclassical limit of the dynamics via asymptotic approximation methods.

25 pages, 5 figures in color

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Cited by in corpus (7)

• Boosting Wigner's nj-symbols
• Spin foam amplitude of the black-to-white hole transition
• Classical dynamics for Loop Gravity: The 2-vertex model
• On the polymer quantization of connection theories: graph coherent states
• Introduction to SU(2) recoupling theory and graphical methods for loop quantum gravity
• Probing the Shape of Quantum Surfaces: the Quadrupole Moment Operator
• Deformations of Lorentzian Polyhedra: Kapovich-Millson phase space and SU(1,1) Intertwiners