Area is the length of Ashtekar’s triad field

Carlo Rovelli
Phys. Rev. D 47, 1703 – Published 15 February 1993; Erratum Phys. Rev. D 87, 089902 (2013)
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Abstract

The variables introduced by Ashtekar in general relativity have several useful and nice properties. We point out a further feature of these variables: the so(3)-invariant norm of the variable conjugate to Ashtekar’s connection, namely, the inverse densitized triad or the analogue of the electric field, is the area two-form; that is, it is the two-form that gives physical area to any surface. The new variables naturally determine areas in the same way in which the metric tensor naturally determines lengths.

  • Received 26 August 1992

DOI:https://doi.org/10.1103/PhysRevD.47.1703

©1993 American Physical Society

Erratum

Authors & Affiliations

Carlo Rovelli

  • Physics Department, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
  • Dipartimento di Fisica, Universita’ di Trento, and Istituto Nazionale di Fisica Nucleare, INFN, Sezione di Padova, Italy

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Issue

Vol. 47, Iss. 4 — 15 February 1993

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