Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity

@article{Thiemann1996AnomalyfreeFO,
  title={Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity},
  author={Thomas Thiemann},
  journal={Physics Letters B},
  year={1996},
  volume={380},
  pages={257-264}
}
  • T. Thiemann
  • Published 29 June 1996
  • Physics
  • Physics Letters B
View PDF on arXiv
290 Citations
Highly Influential Citations
15
Background Citations
112
Methods Citations
40
Results Citations
1

290 Citations

Affine group representation formalism for four-dimensional, Lorentzian, quantum gravity
Within the context of the Ashtekar variables, the Hamiltonian constraint of four-dimensional pure general relativity with cosmological constant, Λ, is re-expressed as an affine algebra with the…
String theory in a vertex operator representation: a simple model for testing loop quantum gravity
The loop quantum gravity technique is applied to the free bosonic string. A Hilbert space similar to loop space in loop quantum gravity as well as representations of diffeomorphism and hamiltonian…
Anomaly freedom in perturbative loop quantum gravity
A fully consistent linear perturbation theory for cosmology is derived in the presence of quantum corrections as they are suggested by properties of inverse volume operators in loop quantum gravity.…
Loop quantum cosmology: I. Kinematics
The framework of quantum symmetry reduction is applied to loop quantum gravity with respect to transitively acting symmetry groups. This allows us to test loop quantum gravity in a large class of…
Loop quantum cosmology: I. Kinematics
The framework of quantum symmetry reduction is applied to loop quantum gravity with respect to transitively acting symmetry groups. This allows us to test loop quantum gravity in a large class of…
Matrix elements of Lorentzian Hamiltonian constraint in loop quantum gravity
The Hamiltonian constraint is the key element of the canonical formulation of LQG coding its dynamics. In Ashtekar-Barbero variables it naturally splits into the so called Euclidean and Lorentzian…
The conformal factor in the parameter-free construction of spin-gauge variables for gravity
The newly found conformal decomposition in canonical general relativity is applied to drastically simplify the recently formulated parameter-free construction of spin-gauge variables for gravity. The…
Quantum Gravity as the Natural Regulator of Matter Quantum Field Theories
It is an old speculation in physics that, once the gravitational field is successfully quantized, it should serve as the natural regulator of infrared and ultraviolet singularities that plague…
Ja n 20 02 String theory in a vertex operator representation : a simple model for testing loop quantum gravity
The loop quantum gravity technique is applied to the free bosonic string. A Hilbert space similar to loop space in loop quantum gravity as well as representations of diffeomorphism and hamiltonian…
Quantum spin dynamics (QSD) V: Quantum Gravity as the natural regulator of the Hamiltonian constraint of matter quantum field theories
It is an old speculation in physics that, once the gravitational field is successfully quantized, it should serve as the natural regulator of infrared and ultraviolet singularities that plague…
...
...

References

SHOWING 1-10 OF 53 REFERENCES
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…
Constraint quantization of parametrized relativistic gauge systems in curved spacetimes.
The Dirac constraint quantization of a finite-dimensional relativistic gauge system with a quadratic super-Hamiltonian and linear supermomenta is investigated as a model for quantizing generally…
A length operator for canonical quantum gravity
We construct an operator that measures the length of a curve in four-dimensional Lorentzian vacuum quantum gravity. We work in a representation in which an SU(2) connection is diagonal and it is…
Real alternative to quantum gravity in loop space.
  • Loll
  • Physics
    Physical review. D, Particles and fields
  • 1996
We show that the Hamiltonian of four-dimensional Lorentzian gravity, defined on a space of real, SU(2)-valued connections, in spite of its non-polynomiality possesses a natural quantum analogue in a…
Spin networks and quantum gravity.
  • Rovelli, Smolin
  • Physics
    Physical review. D, Particles and fields
  • 1995
TLDR
A new basis on the state space of non-perturbative quantum gravity is introduced that allows a simple expression for the exact solutions of the Hamiltonian constraint (Wheeler-DeWitt equation) that have been discovered in the loop representation.
The physical Hamiltonian in nonperturbative quantum gravity.
A quantum Hamiltonian which evolves the gravitational field according to time as measured by constant surfaces of a scalar field is defined through a regularization procedure based on the loop…
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…
Transversal affine connection and quantization of constrained systems
The Dirac quantization of a finite‐dimensional relativistic system with a quadratic super‐Hamiltonian and linear supermomenta is investigated. In a previous work, the operator constraints were…
Quantum linearization instabilities of de Sitter spacetime. II
It is known that all the physical states in linearized gravity are required to be invariant under the continuous isometries of the background spacetime if it is spatially compact. For example, all…
Discreteness of area and volume in quantum gravity [Nucl. Phys. B 442 (1995) 593]
...
...