# Quantum Geometry

@article{FockQuantumG, title={Quantum Geometry}, author={Vladimir V. Fock and D. Iwanenko}, journal={Nature}, volume={123}, pages={838-838} }

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.

## 154 Citations

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

- PhysicsJournal of Physics: Conference Series
- 2019

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

- Physics
- 2005

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

- Mathematics, Physics
- 2020

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

- Physics
- 2004

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

- Physics, Mathematics
- 2005

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

- Mathematics
- 1996

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

- PhysicsLiving 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

- Mathematics
- 2002

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

- Mathematics
- 1995

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…