Eur. Phys. J. C (2012) 72: 2079
https://doi.org/10.1140/epjc/s10052-012-2079-x

Regular Article - Theoretical Physics

Geometrical properties of Riemannian superspaces, observables and physical states

¹ International Institute of Physics, Natal, RN, Brazil
² Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980, Dubna, Russian Federation

^* e-mail: diego@iip.ufrn.br
^** e-mail: diego@theor.jinr.ru

Received: 18 May 2012
Published online: 20 July 2012

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.