• Corpus ID: 239049690

Scalar curvature operator for models of loop quantum gravity on a cubical graph

@inproceedings{Lewandowski2021ScalarCO,
  title={Scalar curvature operator for models of loop quantum gravity on a cubical graph},
  author={Jerzy Lewandowski and Ilkka Makinen},
  year={2021}
}
In this article we introduce a new operator representing the three-dimensional scalar curvature in loop quantum gravity. Our construction does not apply to the entire kinematical Hilbert space of loop quantum gravity; instead, the operator is defined on the Hilbert space of a fixed cubical graph. The starting point of our work is to write the spatial Ricci scalar classically as a function of the densitized triad. We pass from the classical expression to a quantum operator through a… 

Figures from this paper

References

SHOWING 1-10 OF 33 REFERENCES
New scalar constraint operator for loop quantum gravity
We present a concrete and explicit construction of a new scalar constraint operator for loop quantum gravity. The operator is defined on the recently introduced space of partially diffeomorphism
A curvature operator for LQG
Loop Quantum Gravity [1] is a promising candidate to finally realize a quantum description of General Relativity. The theory presents two complementary descriptions based on the canonical and the
FUNDAMENTAL STRUCTURE OF LOOP QUANTUM GRAVITY
In the recent twenty years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. The aim of loop quantum gravity is
Hamiltonian operator for loop quantum gravity coupled to a scalar field
We present the construction of a physical Hamiltonian operator in the deparametrized model of loop quantum gravity coupled to a free scalar field. This construction is based on the use of the
Algebraic quantum gravity (AQG): IV. Reduced phase space quantization of loop quantum gravity
We perform a canonical, reduced phase space quantization of general relativity by loop quantum gravity (LQG) methods. The explicit construction of the reduced phase space is made possible by the
Algebraic Quantum Gravity (AQG). I. Conceptual Setup
We introduce a new top down approach to canonical quantum gravity, called algebraic quantum gravity (AQG). The quantum kinematics of AQG is determined by an abstract *-algebra generated by a
Discreteness of area and volume in quantum gravity [Nucl. Phys. B 442 (1995) 593]
Abstract We study the operator that corresponds to the measurement of volume, in non-perturbative quantum gravity, and we compute its spectrum. The operator is constructed in the loop representation,
Quantum Spin Dynamics (QSD)
An anomaly-free operator corresponding to the Wheeler - DeWitt constraint of Lorentzian, four-dimensional, canonical, non-perturbative vacuum gravity is constructed in the continuum. This operator is
The Length operator in Loop Quantum Gravity
Abstract The dual picture of quantum geometry provided by a spin network state is discussed. From this perspective, we introduce a new operator in Loop Quantum Gravity—the length operator. We
Effective dynamics from coherent state path integral of full loop quantum gravity
A new routine is proposed to relate loop quantum cosmology (LQC) to loop quantum gravity (LQG) from the perspective of effective dynamics. We derive the big-bang singularity resolution and big bounce
...
1
2
3
4
...