ON GRAVITO-ELECTROMAGNETIC DUALITY IN GENERAL RELATIVITY

In analogy with the electromagnetic theory, we resolve the Riemann curvature into electric and magnetic parts and consider the analogous duality transformation which keeps the Einstein action for vacuum invariant. It is remarkable that the duality symmetry of the action also leads to the vacuum field equation without cosmological constant. Further invariance of the vacuum equation and the action under the gravito-electric duality require gravitational constant to change sign.

A Bosonisation of QCD and Realisations of Chiral Symmetry

We employ the functional integral formalism to study quantum chromodynamics (QCD) with Nf quarks of zero bare mass. In addition to local SU(Nc) colour symmetry, this theory possesses exact global G = UdNf)@UR(Nf) chiral symmetry. We obtain an exact bilocal Bose field representation of the generating functional which, as we prove after establishing the manner in which the bilocal fields transform under G, preserves the global chiral symmetry. We demonstrate how a local Bose field representation of the generating functional may be obtained from the bilocal bosonisation. This provides a direct link between QCD and low energy meson phenomenological models. We utilise the bilocal bosonisation in the study of the dynamical breakdown of the global chiral symmetry group G. We derive the vacuum field equation from the exact bilocal Bose field effective action and discuss two alternative solutions: one corresponding to a Wigner-Weyl realisation of the global symmetry group G in which the vacuum configuration is invariant under G; the other to a mixed realisation in which the vacuum manifold is the coset space G/H = U A(Nf ), where H = Uv(Nf ) is a subgroup of G.