• DOI:10.1007/978-3-540-47295-7_2
• Corpus ID: 17150040

Canonical Quantum Gravity

@inproceedings{Zanelli1985CanonicalQG,
  title={Canonical Quantum Gravity},
  author={Jorge Zanelli},
  year={1985}
}

• J. Zanelli
• Published 1985
• Physics

This is a review of the aspirations and disappointments of the canonical quantization of geometry. I compare the two chief ways of looking at canonical gravity, geometrodynamics and connection dynamics. I capture as much of the classical theory as I can by pictorial visualization. Algebraic aspects dominate my description of the quantization program. I address the problem of observables. The reader is encouraged to follow the broad outlines and not worry about the technical details. CLASSICAL CANONICAL GRAVITY Dynamical laws and instantaneous laws One of the main preoccupations of classical physics has been finding the laws governing physical data. One of the oldest schemes of quantization has been to subject such data to canonical commutation relations. I am going to review where this program leads us when it is applied to geometry. Classical physics deals with two kinds of laws: dynamical laws, and instantaneous laws. The discovery of dynamical laws started the Newtonian revolution. The first instantaneous law was found by Gauss: at any instant of time, the divergence of the electric field is determined by the distribution of charges. In empty space, the instantaneous electric field is divergence-free.