Conservative quantities and their algebra in the self-dual gravity. (English) Zbl 0828.53073
Summary: A general covariant conservation law of energy-momentum in complex general relativity is obtained by way of general displacement transformation in terms of Ashtekar’s new variables. The energy is exactly the ADM Hamiltonian on the constraint surface under the condition that an appropriate time function is chosen. The energy-momentum is gauge covariant and commutes with all the constraints, whence they are physical observables. Furthermore, the Poisson brackets of the momentum and the internal SU(2) charges form a 3-Poincaré algebra.
MSC:
| 53Z05 | Applications of differential geometry to physics |
| 83C40 | Gravitational energy and conservation laws; groups of motions |
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