Fock representation of gravitational boundary modes and the discreteness of the area spectrum

Abstract

In this article, we study the quantum theory of gravitational boundary modes on a null surface. These boundary modes are given by a spinor and a spinor-valued two-form, which enter the gravitational boundary term for self-dual gravity. Using a Fock representation, we quantise the boundary fields, and show that the area of a two-dimensional cross section turns into the difference of two number operators. The spectrum is discrete, and it agrees with the one known from loop quantum gravity with the correct dependence on the Barbero--Immirzi parameter. No discrete structures (such as spin network functions, or triangulations of space) are ever required---the entire derivation happens at the level of the continuum theory. In addition, the area spectrum is manifestly Lorentz invariant.

27 pages, two figures

References in corpus (7)

• The loop-quantum-gravity vertex-amplitude
• Flipped spinfoam vertex and loop gravity
• From twistors to twisted geometries
• Quanta of Geometry: Noncommutative Aspects
• Discreteness of area in noncommutative space
• Loop expansion and the bosonic representation of loop quantum gravity
• Quantum gravity at the corner

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• Internal quantum reference frames for finite Abelian groups
• Quantum Null Geometry and Gravity
• Quantum Reference Frames at the Boundary of Spacetime
• Sachs' free data in real connection variables
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