Lagrange multipliers in theories of gravitation
In gravitatinal theories, P-italic-variation (independepent variation of metric and connection) and H-variation (variation of the metric alone) may be reconciled through C-italic-variation (use of Lagrange multipliers ..lambda.. in P-italic-variation). We extend C-italic-variation to fields coupled with gravitational field and elucidate the cases of vanishing ..lambda... We show that the interpretation of ..lambda.. as constraint reaction forces sheds new light on the structure of these theories; we are thus led to question the necessary of relating torsion to spin, and as an alternative to the theory of Dirac particles in Einstein-Cartan space-time, we propose in a Lorentzian space-time a theory in which Lagrange multipliers corresponding to the vanishing of torsion lead to the symmetrization of canonical energy-momentum tensor and avoid the Heisenberg-Pauli-type terms. Lagrange multipliers also serve to reduce the fourth-order differential equations of gravitational quadratic Lagrangians to second-order ones with additional field variables (a scalar P-italic and a traceless tensor P-italic-tilde/sub i//sub j/); this reduction helps to make precise the compatibility of these theories with General Relativity. Simple derivations are also given for Chern and Euler characteristics c-italic/sub 2/ and /sub Chi//sub 2/, and for other identities.
- Research Organization:
- Unite-acute-accent Associe-acute-accente au CNRS n 769, Universite-acute-accent P. et M. Curie, Laboratoire de Physique The-acute-accentorique, Institut Henri Poincare-acute-accent, 11, rue Pierre et Marie Curie, 75231 Paris Cedex 05, France
- OSTI ID:
- 5567075
- Journal Information:
- Ann. Phys. (N.Y.); (United States), Vol. 168:2
- Country of Publication:
- United States
- Language:
- English
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