Journal of Low Temperature Physics

, Volume 119, Issue 3–4, pp 241–247 | Cite as

Momentum-Space Topology of Standard Model

  • G. E. Volovik


The momentum-space topological invariants, which characterize the ground state of the Standard Model, are continuous functions of two parameters, generated by the hypercharge and by the weak charge. These invariants provide the absence of the mass of the elementary fermionic particles in the symmetric phase above the electroweak transition (the mass protection). All the invariants become zero in the broken symmetry phase, as a result all the elementary fermions become massive. Relation of the momentum-Space invariants to chiral anomaly is also discussed.


Continuous Function Magnetic Material Break Symmetry Symmetry Phase Topological Invariant 
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  1. 1.
    G.E. Volovik, Proc. Natl. Acad. Sc. USA 96, 6042 (1999); 3 He and Universe parallelism”, cond-mat/9902171.Google Scholar
  2. 2.
    A.A. Abrikosov, Phys. Rev. B 58, 2788 (1998).Google Scholar
  3. 3.
    C.D. Froggatt, and H. B. Nielsen, “Why do we have parity violation?”, hepph/9906466.Google Scholar
  4. 4.
    K. Ishikawa and T. Matsuyama, Z. Phys. C 33, 41 (1986); Nuclear Physics B 280, 532 (1987).Google Scholar
  5. 5.
    G.E. Volovik and V.M. Yakovenko,“Fractional charge, spin and statistics of solitons in superfluid 3 He film,” J. Phys.: Cond. Matter 1,5263 (1989); G.E. Volovik, “Exotic properties of superfluid 3 He” (World Scientific, Singapore-New Jersey-London-Hong Kong, 1992), Chapter 9.Google Scholar
  6. 6.
    V.M. Yakovenko, “Spin, Statistics and Charge of Solitons in (2+1)-Dimensional Theories”, Fizika (Zagreb) 21,suppl. 3, 231 (1989) [cond-mat/97-3195].Google Scholar
  7. 7.
    T.M.P. Tait, “Signals for the Electroweak Symmetry Breaking Associated with the Top Quark”, hep-ph/9907462.Google Scholar
  8. 8.
    R. Foot, H. Lew, and R.R. Volkas, “Models of extended Pati-Salam gauge symmetry”, Phys. Rev. D 44, 859 (1991).Google Scholar

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • G. E. Volovik
    • 1
    • 2
  1. 1.Low Temperature LaboratoryHelsinki University of TechnologyHUTFinland
  2. 2.L.D. Landau Institute for Theoretical PhysicsMoscowRussia

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