On the solution of the initial value constraints for general relativity coupled to matter in terms of Ashtekar's variables

Abstract

The method of solution of the initial value constraints for pure canonical gravity in terms of Ashtekar's new canonical variables due to CDJ is further developed in the present paper. There are 2 new main results : 1) We extend the method of CDJ to arbitrary matter-coupling again for non-degenerate metrics : the new feature is that the 'CDJ-matrix' adopts a nontrivial antisymmetric part when solving the vector constraint and that the Klein-Gordon-field is used, instead of the symmetric part of the CDJ-matrix, in order to satisfy the scalar constraint. 2) The 2nd result is that one can solve the general initial value constraints for arbitrary matter coupling by a method which is completely independent of that of CDJ. It is shown how the Yang-Mills and gravitational Gauss constraints can be solved explicitely for the corresponding electric fields. The rest of the constraints can then be satisfied by using either scalar or spinor field momenta. This new trick might be of interest also for Yang-Mills theories on curved backgrounds.

Latex, 15 pages, PITHA93-1, January 93

References in corpus (1)

• Canonical Quantization of Spherically Symmetric Gravity in Ashtekar's Self-Dual Representation

Cited by in corpus (4)

• Finite states in four dimensional quantized gravity
• Bibliography of Publications related to Classical and Quantum Gravity in terms of the Ashtekar Variables
• Bibliography of publications related to Classical and Quantum Gravity in terms of Connection and Loop Variables
• Finite states in four dimensional quantum gravity. The isotropic minisuperspace Asktekar--Klein--Gordon model