Geometrical properties of Riemannian superspaces, observables and physical states

Abstract

Classical and quantum aspects of physical systems that can be described by Riemannian non-degenerate superspaces are analyzed from the topological and geometrical points of view. For the N=1 case the simplest supermetric introduced by Cirilo-Lombardo (Phys. Lett. B 661:186, 2008) have the correct number of degrees of freedom for the fermion fields and the super-momentum fulfills the mass shell condition, in sharp contrast with other cases in the literature where the supermetric is degenerate. This fact leads a deviation of the 4-impulse (e.g. mass constraint) that can be mechanically interpreted as a modification of the Newton law. Quantum aspects of the physical states and the basic states, and the projection relation between them, are completely described due the introduction of a new Majorana–Weyl representation of the generators of the underlying group manifold. A new oscillatory fermionic effect in the B 0 part of the vacuum solution involving the chiral and antichiral components of this Majorana bispinor is explicitly shown.