On the Implementation of the Canonical Quantum Simplicity Constraint

@article{Bodendorfer2013OnTI,
  title={On the Implementation of the Canonical Quantum Simplicity Constraint},
  author={Norbert Bodendorfer and Thomas Thiemann and Andreas Thurn},
  journal={Classical and Quantum Gravity},
  year={2013},
  volume={30},
  pages={045005}
}
In this paper, we discuss several approaches to solve the quadratic and linear simplicity constraints in the context of the canonical formulations of higher dimensional general relativity and supergravity developed in our companion papers. Since the canonical quadratic simplicity constraint operators have been shown to be anomalous in any dimension D ⩾ 3 in Class. Quantum Grav. 30 045003, non-standard methods have to be employed to avoid inconsistencies in the quantum theory. We show that one… 

Figures from this paper

New variables for classical and quantum gravity in all dimensions: I. Hamiltonian analysis
We rederive the results of our companion paper, for matching space–time and internal signature, by applying in detail the Dirac algorithm to the Palatini action. While the constraint set of the
New Variables for Classical and Quantum Gravity in all Dimensions II. Lagrangian Analysis
We rederive the results of our companion paper, for matching spacetime and internal signature, by applying in detail the Dirac algorithm to the Palatini action. While the constraint set of the
New variables for classical and quantum gravity in all dimensions: IV. Matter coupling
We employ the techniques introduced in the companion papers [1, 2, 3] to derive a connection formulation of Lorentzian General Relativity coupled to Dirac fermions in dimensions D + 1 ≥ 3 with
Towards Loop Quantum Supergravity (LQSG) II. p-Form Sector
In our companion paper, we focused on the quantization of the Rarita–Schwinger sector of supergravity theories in various dimensions by using an extension of loop quantum gravity to all spacetime
Coherent intertwiner solution of simplicity constraint in all dimensional loop quantum gravity
We propose a new treatment of the quantum simplicity constraints appearing in the general ${SO(D+1)}$ formulation of loop quantum gravity for the ${(1+D)}$-dimensional space-time. Instead of strongly
Twistorial structure of loop-gravity transition amplitudes
The spin foam formalism provides transition amplitudes for loop quantum gravity. Important aspects of the dynamics are understood, but many open questions are pressing on. In this paper we address
New variables for classical and quantum (super)-gravity in all dimensions
Supergravity was originally introduced in the hope of finding a theory of gravity without the shortcoming of perturbative non-renormalisability. Although this goal does not seem to have been reached
Towards Loop Quantum Supergravity (LQSG) I. Rarita-Schwinger Sector
In our companion papers, we managed to derive a connection formulation of Lorentzian general relativity in D + 1 dimensions with compact gauge group SO(D + 1) such that the connection is
On the role of the Barbero-Immirzi parameter in discrete quantum gravity
The one-parameter family of transformations identified by Barbero and Immirzi plays a significant role in non-perturbative approaches to quantum gravity, among them loop quantum gravity and spin
Higher dimensional and supersymmetric extensions of loop quantum gravity
In this work, we extend loop quantum gravity (LQG) both, to higher dimensions and supersymmetry (i.e. supergravity theories), thus overcoming the current limitation to 3+1 dimensions with standard
...
1
2
3
4
...

References

SHOWING 1-10 OF 66 REFERENCES
New variables for classical and quantum gravity in all dimensions: I. Hamiltonian analysis
We rederive the results of our companion paper, for matching space–time and internal signature, by applying in detail the Dirac algorithm to the Palatini action. While the constraint set of the
New Variables for Classical and Quantum Gravity in all Dimensions II. Lagrangian Analysis
We rederive the results of our companion paper, for matching spacetime and internal signature, by applying in detail the Dirac algorithm to the Palatini action. While the constraint set of the
Quantum spin dynamics: VIII. The master constraint
Recently the master constraint programme (MCP) for loop quantum gravity (LQG) was launched which replaces the infinite number of Hamiltonian constraints by a single master constraint. The MCP is
Simplicity in simplicial phase space
A key point in the spin foam approach to quantum gravity is the implementation of simplicity constraints in the partition functions of the models. Here, we discuss the imposition of these constraints
New variables for classical and quantum gravity in all dimensions: IV. Matter coupling
We employ the techniques introduced in the companion papers [1, 2, 3] to derive a connection formulation of Lorentzian General Relativity coupled to Dirac fermions in dimensions D + 1 ≥ 3 with
Revisiting the simplicity constraints and coherent intertwiners
TLDR
This work applies the recently developed U(N) framework for SU(2) intertwiners to the issue of imposing the simplicity constraints to spin network states and proposes a set of U( N) coherent states that solves all the simplicity constraint weakly for an arbitrary Immirzi parameter.
Towards Loop Quantum Supergravity (LQSG) II. p-Form Sector
In our companion paper, we focused on the quantization of the Rarita–Schwinger sector of supergravity theories in various dimensions by using an extension of loop quantum gravity to all spacetime
Hilbert space structure of covariant loop quantum gravity
We investigate Hilbert space in the Lorentz covariant approach to loop quantum gravity. We restrict ourselves to the space where all area operators are simultaneously diagonalizable, assuming that it
BF Description of Higher-Dimensional Gravity Theories
It is well known that, in the first-order formalism, pure three-dimensional gravity is just the BF theory. Similarly, four-dimensional general relativity can be formulated as BF theory with an
Towards Loop Quantum Supergravity (LQSG) I. Rarita-Schwinger Sector
In our companion papers, we managed to derive a connection formulation of Lorentzian general relativity in D + 1 dimensions with compact gauge group SO(D + 1) such that the connection is
...
1
2
3
4
5
...