Field Theories found Geometrically from Embeddings in Flat Frame Bundles

Details Field Theories found Geometrically from Embeddings in Flat Frame Bundles Field Theories found Geometrically from Embeddings in Flat Frame Bundles

2006-12-19

arxiv.org/abs/gr-qc/0612113v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

has appeared in J. Calmet, W. M. Seiler and R. W. Tucker (Eds.), Global Integrability of Field Theories (Proceedings of GIFT 2

Scientific paper

We present two families of exterior differential systems (EDS) for non-isometric embeddings of orthonormal frame bundles over Riemannian spaces of dimension q = 2, 3, 4, 5.... into orthonormal frame bundles over flat spaces of sufficiently higher dimension. We have calculated Cartan characters showing that these EDS satisfy Cartan's test and are well-posed dynamical field theories. The first family includes a constant-coefficient (cc) EDS for classical Einstein vacuum relativity (q = 4). The second family is generated only by cc 2-forms, so these are integrable (but nonlinear) systems of partial differential equations. These calibrated field theories apparently are new, although the simplest case q = 2 turns out to embed a ruled surface of signature (1,1) in flat space of signature (2,1). Cartan forms are found to give explicit variational principles for all these dynamical theories.

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