Geometrical properties of Riemannian superspaces, observables and physical states
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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.
KeywordsCoherent State Fermionic Momentum Evolution Parameter Group Manifold Quantum Aspect
Many thanks are given to Professors Yu.P. Stepanovsky, John Klauder and E.C.G. Sudarshan for their interest; and particularly to Dr. Victor I. Afonso for several discussions in the subject and help me in the preparation of this text. This work is in memory of Anna Grigorievna Kartavenko, one of the main responsible scientists of the International Department of the Joint Institute of Nuclear Research, who passed away recently. She was as part of my family in Dubna: an angel that helped me in several troubles.
The author is partially supported by CNPQ–Brazilian funds.