Null Surface Canonical Formalism
Part of the
Ettore Majorana International Science Series
book series (EMISS, volume 56)
More than 20 years ago, Peter Bergmann together with one of us (JNG) considered the problem of constructing the canonical formalism for general relativity on a null cone. The motivation for doing so came from the difficulty in constructing the observables which could then become the basic operators in a quantum theory of gravity. The analysis of Bondi1, Sachs2, and Newman-Unti3 of the Einstein equa-tions in the vicinity of null infinity indicated that the constraint equations were easy to integrate and that the data to be specified freely was easily recognizable. On the outgoing null cone, the geometry of the 2-surface foliation is given and at null infinity one gives the news function at all times and the mass aspect and the dipole aspect at one time. This result gave hope that in the canonical formalism one would be able to recognize the appropriate variables for the quantum theory.
KeywordsPoisson Bracket Class Constraint Dirac Bracket Null Cone Secondary Constraint
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