Geometrical properties of Riemannian superspaces, observables and physical states

  • Diego Julio Cirilo-LombardoEmail author
Regular Article - Theoretical Physics


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.


Coherent State Fermionic Momentum Evolution Parameter Group Manifold Quantum Aspect 
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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.


  1. 1.
    D.J. Cirilo-Lombardo, Found. Phys. 37, 919 (2007) MathSciNetADSzbMATHCrossRefGoogle Scholar
  2. 2.
    D.J. Cirilo-Lombardo, Phys. Lett. B 661, 186 (2008) MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    A.I. Pashnev, D.V. Volkov, Teor. Mat. Fiz. 44, 321 (1980) MathSciNetGoogle Scholar
  4. 4.
    R. Casalbuoni, Phys. Lett. B 62, 49 (1976) MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    L. Brink, J.H. Schwartz, Phys. Lett. B 100, 310 (1981) MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    W. Siegel, Phys. Lett. B 203, 79 (1988) MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    D.J. Cirilo-Lombardo, V.I. Afonso, work in preparation Google Scholar
  8. 8.
    D.J. Cirilo-Lombardo, work in progress Google Scholar
  9. 9.
    T.F. Jordan, N. Mukunda, S.V. Pepper, J. Math. Phys. 4, 1089 (1963) MathSciNetADSzbMATHCrossRefGoogle Scholar
  10. 10.
    D.J. Cirilo-Lombardo, Found. Phys. 39, 373 (2009) MathSciNetADSzbMATHCrossRefGoogle Scholar
  11. 11.
    V.D. Gershun, D.J. Cirilo-Lombardo, J. Phys. A 43, 305401 (2010) MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag / Società Italiana di Fisica 2012

Authors and Affiliations

  1. 1.International Institute of PhysicsNatalBrazil
  2. 2.Bogoliubov Laboratory of Theoretical PhysicsJoint Institute for Nuclear ResearchDubnaRussian Federation

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