Fock Representation of Gravitational Boundary Modes and the Discreteness of the Area Spectrum

@article{Wieland2017FockRO,
  title={Fock Representation of Gravitational Boundary Modes and the Discreteness of the Area Spectrum},
  author={Wolfgang Wieland},
  journal={Annales Henri Poincar{\'e}},
  year={2017},
  volume={18},
  pages={3695-3717}
}
  • W. Wieland
  • Published 1 June 2017
  • Physics
  • Annales Henri Poincaré
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… 
View on Springer
arxiv.org
35 Citations
Highly Influential Citations
1
Background Citations
16
Methods Citations
2

35 Citations

Conformal boundary conditions, loop gravity and the continuum
  • W. Wieland
  • Physics
    Journal of High Energy Physics
  • 2018
A bstractIn this paper, we will make an attempt to clarify the relation between three-dimensional euclidean loop quantum gravity with vanishing cosmological constant and quantum field theory in the…
Quantum gravity in three dimensions, Witten spinors and the quantisation of length
New boundary variables for classical and quantum gravity on a null surface
The covariant Hamiltonian formulation for general relativity is studied in terms of self-dual variables on a manifold with an internal and lightlike boundary. At this inner boundary, new canonical…
A pr 2 01 8 Loop quantum gravity and the continuum
In this paper, we will make an attempt to clarify the relation between three-dimensional euclidean loop quantum gravity with vanishing cosmological constant and quantum field theory in the continuum.…
Gravitational SL(2, ℝ) algebra on the light cone
  • W. Wieland
  • Physics
    Journal of High Energy Physics
  • 2021
Abstract In a region with a boundary, the gravitational phase space consists of radiative modes in the interior and edge modes at the boundary. Such edge modes are necessary to explain how the…
Deformed Heisenberg charges in three-dimensional gravity
We consider the bulk plus boundary phase space for three-dimensional gravity with negative cosmological constant for a particular choice of conformal boundary conditions: the conformal class of the…
Boundary effects in General Relativity with tetrad variables
Varying the gravitational Lagrangian produces a boundary contribution that has various physical applications. It determines the right boundary terms to be added to the action once boundary conditions…
Edge modes of gravity. Part III. Corner simplicity constraints
In the tetrad formulation of gravity, the so-called simplicity constraints play a central role. They appear in the Hamiltonian analysis of the theory, and in the Lagrangian path integral when…
Generating functional for gravitational null initial data
  • W. Wieland
  • Physics
    Classical and Quantum Gravity
  • 2019
A field theory on a three-dimensional manifold is introduced, whose field equations are the constraint equations for general relativity on a three-dimensional null hypersurface. The underlying…
Edge modes of gravity. Part II. Corner metric and Lorentz charges
In this second paper of the series we continue to spell out a new program for quantum gravity, grounded in the notion of corner symmetry algebra and its representations. Here we focus on tetrad…
...
...

References

SHOWING 1-10 OF 32 REFERENCES
Discrete gravity as a topological field theory with light-like curvature defects
A bstractI present a model of discrete gravity as a topological field theory with defects. The theory has no local degrees of freedom and the gravitational field is trivial everywhere except at a…
Quantum Gravity at the Corner
We investigate the quantum geometry of a 2d surface S bounding the Cauchy slices of a 4d gravitational system. We investigate in detail for the first time the boundary symplectic current that…
New boundary variables for classical and quantum gravity on a null surface
The covariant Hamiltonian formulation for general relativity is studied in terms of self-dual variables on a manifold with an internal and lightlike boundary. At this inner boundary, new canonical…
Local subsystems in gauge theory and gravity
A bstractWe consider the problem of defining localized subsystems in gauge theory and gravity. Such systems are associated to spacelike hypersurfaces with boundaries and provide the natural setting…
Quasi-local gravitational angular momentum and centre of mass from generalised Witten equations
Witten’s proof for the positivity of the ADM mass gives a definition of energy in terms of three-surface spinors. In this paper, we give a generalisation for the remaining six Poincaré charges at…
Quantum theory of geometry: I. Area operators
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated…
Discreteness of area and volume in quantum gravity [Nucl. Phys. B 442 (1995) 593]
Edge modes and corner ambiguities in 3d Chern–Simons theory and gravity
Quantum geometry of isolated horizons and black hole entropy
Using the earlier developed classical Hamiltonian framework as the point of departure, we carry out a non-perturbative quantization of the sector of general relativity, coupled to matter, admitting…
Uniqueness of Diffeomorphism Invariant States on Holonomy–Flux Algebras
Loop quantum gravity is an approach to quantum gravity that starts from the Hamiltonian formulation in terms of a connection and its canonical conjugate. Quantization proceeds in the spirit of Dirac:…
...
...