Canonical quantization of 1+1 dimensional gravity

Tom Banks, Leonard Susskind

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


Based on Polyakov's evaluation of the Fadeev-Popov determinant for (1+1)-dimensional gravity in the conformal gauge we formulate a canonical quantization in the synchronous gauge. We find that the system is describable as a quantum mechanical system of one degree of freedom. The quantization can be carried out and solved when any number of gauge fields are included. Scalar and spinor fields lead to new difficulties. For positive cosmological constant the geometry collapses as suggested by the classical system. For negative cosmological constant a more interesting behavior involving exponentially expanding and contracting universes occurs.

Original languageEnglish (US)
Pages (from-to)475-496
Number of pages22
JournalInternational Journal of Theoretical Physics
Issue number5
StatePublished - May 1984
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Physics and Astronomy (miscellaneous)


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