Classical higgs fields
Article
First Online:
Received:
Revised:
- 60 Downloads
- 3 Citations
Abstract
We consider a classical gauge theory on a principal fiber bundle P → X in the case where its structure group G is reduced to a subgroup H in the presence of classical Higgs fields described by global sections of the quotient fiber bundle P/H → X. We show that matter fields with the exact symmetry group H in such a theory are described by sections of the composition fiber bundle Y → P/H → X, where Y → P/H is the fiber bundle with the structure group H, and the Lagrangian of these sections is factored by virtue of the vertical covariant differential determined by a connection on the fiber bundle Y → P/H.
Keywords
gauge field Higgs field matter field fiber bundle connectionPreview
Unable to display preview. Download preview PDF.
References
- 1.G. Sardanashvily, Internat. J. Geom. Meth. Mod. Phys., 5, v–xvi (2008).CrossRefMATHGoogle Scholar
- 2.G. Sardanashvily, Internat. J. Geom. Meth. Mod. Phys., 5, 1163–1189 (2008).CrossRefMATHMathSciNetGoogle Scholar
- 3.G. Giachetta, L. Mangiarotti, and G. Sardanashvily, Advanced Classical Field Theory, World Scientific, Singapore (2009).CrossRefMATHGoogle Scholar
- 4.L. Mangiarotti and G. Sardanashvily, Connections in Classical and Quantum Field Theory, World Scientific, Singapore (2000).CrossRefMATHGoogle Scholar
- 5.D. Ivanenko and G. Sardanashvily, Phys. Rep., 94, 1–45 (1983).ADSCrossRefMathSciNetGoogle Scholar
- 6.A. Trautman, Differential Geometry for Physicists (Monogr. Textbooks Phys. Sci., Vol. 2), Bibliopolis, Naples (1984).MATHGoogle Scholar
- 7.M. Keyl, J. Math. Phys., 32, 1065–1071 (1991).ADSCrossRefMATHMathSciNetGoogle Scholar
- 8.G. Sardanashvily, J. Math. Phys., 33, 1546–1549 (1992).ADSCrossRefMathSciNetGoogle Scholar
- 9.G. Sardanashvily, Internat. J. Geom. Meth. Mod. Phys., 3, 139–148 (2006).CrossRefMathSciNetGoogle Scholar
- 10.G. A. Sardanashvily, Theor. Math. Phys., 132, 1163–1171 (2002).CrossRefMATHGoogle Scholar
- 11.G. Sardanashvily, Internat. J. Geom. Meth. Mod. Phys., 8, 1869–1895 (2011).CrossRefMATHMathSciNetGoogle Scholar
- 12.D. J. Saunders, The Geometry of Jet Bundles (London Math. Soc. Lect. Note Ser., Vol. 142), Cambridge Univ. Press, Cambridge (1989).CrossRefMATHGoogle Scholar
- 13.N. Steenrod, The Topology of Fibre Bundles, Princeton Univ. Press, Princeton (1972).Google Scholar
- 14.S. Kobayashi, Transformation Groups in Differential Geometry (Ergeb. Math. ihrer Grenz., Vol. 70), Springer, Berlin (1972).CrossRefMATHGoogle Scholar
- 15.R. Zulanke and P. Wintgen, Differentialgeometrie und Faserbündel (Hochsch. Math., Vol. 75), VEB Deutscher Verlag der Wissenschaften, Berlin (1972).CrossRefGoogle Scholar
- 16.F. Gordejuela and J. Masqué, J. Phys. A, 28, 497–510 (1995).ADSCrossRefMATHGoogle Scholar
- 17.M. Godina and P. Matteucci, J. Geom. Phys., 47, 66–86 (2003); arXiv:math/0201235v2 (2002).ADSCrossRefMATHMathSciNetGoogle Scholar
- 18.S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Wiley, New York (1965).Google Scholar
- 19.G. Sardanashvily and O. Zakharov, Gauge Gravitation Theory, World Scientific, Singapore (1992).CrossRefGoogle Scholar
- 20.G. Sardanashvily, J. Math. Phys., 39, 4874–4890 (1998).ADSCrossRefMATHMathSciNetGoogle Scholar
- 21.G. Mackey, Induced Representations of Groups and Quantum Mechanics, W. A. Benjamin, New York (1968).MATHGoogle Scholar
- 22.S. Coleman, J. Wess, and B. Zumino, Phys. Rev., 177, 2239–2247 (1969).ADSCrossRefGoogle Scholar
- 23.A. Joseph and A. I. Solomon, J. Math. Phys., 11, 748–761 (1970).ADSCrossRefMATHMathSciNetGoogle Scholar
- 24.M. Palese and E. Winterroth, J. Phys.: Conf. Ser., 411, 012025 (2013).ADSGoogle Scholar
Copyright information
© Pleiades Publishing, Ltd. 2014