Quantum Geometry

  title={Quantum Geometry},
  author={Vladimir V. Fock and D. Iwanenko},
DIRAC'S wave equation for the electron involves a Hamiltonian linear in the momenta pk. This fact seems to be of geometrical nature and suggests the introduction of a linear fundamental differential form with matrix coefficients yk in geometrical considerations. 

A Brief Review on Canonical Loop Quantum Gravity: The Kinematical Part

In this article, we briefly review the kinematical part of canonical loop quantum gravity. This article starts with tetradic formulation of gravity both in the covariant approach and canonical

Matrix models, quantum gravity and the spectral dimension

Monte Carlo studies on non-perturbative 2D Euclidean Quantum Gravity can be done with the use of the Dynamical Triangulations method. The Monte Carlo moves defined within the dynamical triangulation

Hilbert bundles as quantum-classical continua

A hybrid quantum–classical model is proposed whereby a micro-structured (Cosserat-type) continuum is construed as a principal Hilbert bundle. A numerical example demonstrates the possible

On Inhomogeneity of a String Bit Model for Quantum Gravity

We study quantum gravitational effect on a two-dimensional open universe with one particle by means of a string bit model. We find that matter is necessarily homogeneously distributed if the

Sum over topologies and double-scaling limit in 2D Lorentzian quantum gravity

A combined non-perturbative path integral over geometries and topologies for two-dimensional Lorentzian quantum gravity that possesses a unique and well-defined double-scaling limit, a property which has eluded similar models of Euclidean quantum gravity in the past.

Reality conditions inducing transforms for quantum gauge field theory and quantum gravity

The algebraic form of the Hamiltonian or Hamiltonian constraint of various (field) theories simplifies considerably if one uses certain complex-valued phase space variables. We show, for a general

Discrete Approaches to Quantum Gravity in Four Dimensions

  • R. Loll
  • Physics
    Living reviews in relativity
  • 1998
Three major areas of research are reviewed: gauge-theoretic approaches, both in a path-integral and a Hamiltonian formulation; quantum Regge calculus; and the method of dynamical triangulations, confining attention to work that is strictly four-dimensional, strictly discrete, and strictly quantum in nature.

Quantization and Intrinsic Dynamics

A dynamical scheme of quantization of symplectic manifolds is described. It is based on intrinsic Schrodinger and Heisenberg type nonlinear evolutionary equations with multidimensional time running

An Account of Transforms on A/G

In this article we summarize and describe the recently found transforms for theories of connections modulo gauge transformations associated with compact gauge groups. Specifically, we put into a