New dynamical variables in Einstein's theory of gravity

We describe an alternative formalism for Einstein's theory of gravity. The role of dynamical variables is played by a collection of ten vector fields $f_{\mu}^A$, $A=1,\dots,10$. The metric is a composite variable, $g_{\mu\nu}=f_{\mu}^Af_{\nu}^A$. The proposed scheme may lead to further progress in a theory of gravity where Einstein's theory is to play the role of an effective theory, with Newton's constant appearing by introducing an anomalous Green's function.