Advertisement

Annales Henri Poincaré

, Volume 20, Issue 12, pp 3955–3996 | Cite as

Mass Gap in Weakly Coupled Abelian Higgs on a Unit Lattice

  • Abhishek GoswamiEmail author
Article

Abstract

The proof of the Higgs mechanism in a weakly coupled lattice gauge theory in \(d \geqslant 2\) is revisited. A new power series cluster expansion is applied, and the mass gap is shown to exist for the observable \(F_{\mu \nu }\).

Mathematics Subject Classification

Primary 81T08 81T13 81T25 

Notes

Acknowledgements

I would like to thank my advisor Jonathan Dimock for his guidance.

References

  1. 1.
    Balaban, T., Imbrie, J., Jaffe, A., Brydges, D.: The mass gap for Higgs models on a unit lattice. Ann. Phys. 158(2), 281–319, 13, 0003-4916 (1984)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    Balaban, T., Feldman, J., Knörrer, H., Trubowitz, E.: Power series representations for bosonic effective actions. J. Stat. Phys. 134, 839 (2009)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Balaban, T., Imbrie, J., Jaffe, A.: Renormalization of the Higgs model: minimizers, propagators, and the stability of mean field theory. Commun. Math. Phys. 97, 299–329 (1985)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    Balaban, T., Imbrie, J., Jaffe, A.: Effective action and cluster properties of the abelian Higgs model. Commun. Math. Phys. 114, 257–315 (1988)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    Brydges, D., Fröhlich, J., Seiler, E.: On the construction of quantized gauge fields. I. General results. Ann. Phys. 121, 227–284 (1979)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    Brydges, D., Fröhlich, J., Seiler, E.: On the construction of quantized gauge fields. II. Convergence of the lattice approximation. Commun. Math. Phys 71(2), 159–205 (1980)ADSCrossRefGoogle Scholar
  7. 7.
    Brydges, D., Fröhlich, J., Seiler, E.: On the construction of quantized gauge fields. III. The two-dimensional abelian Higgs model without cutoffs. Commun. Math. Phys 79, 353–399 (1981)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    Glimm, J., Jaffe, A., Spencer, T.: The particle structure of the weakly coupled \(P(\phi )_{2}\) model and other applications of high temperature expansions, part II: the cluster expansion. In: Wightman, A.S. (ed.) Constructive Quantum Field Theory. Springer Lecture Notes in Physics, vol. 25. Springer, Berlin (1973)Google Scholar
  9. 9.
    Glimm, J., Jaffe, A., Spencer, T.: The Wightman axioms and particle structure in the weakly coupled \(P(\phi )_{2}\) quantum field model. Ann. Math. 100, 585–632 (1974)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Kennedy, T., King, C.: Spontaneous symmetry breakdown in the abelian Higgs model. Commun. Math. Phys. 104(2), 327–347 (1986), 1432-0916ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    Brydges, D., Kennedy, T.: Mayer expansions and the Hamilton–Jacobi equation. J. Stat. Phys. 48, 19–49 (1987)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    Abdesselam, A., Rivasseau, V.: Trees, forests and jungles: a botanical garden for cluster expansions. In: Constructive Physics (Palaiseau, 1994), Lecture Notes in Physics, vol. 446, pp. 7–36. Springer, Berlin (1995)Google Scholar
  13. 13.
    Dimock, J.: The renormalization group according to Balaban—II. Large fields. J. Math. Phys. 54, 092301 (2013)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    Balaban, T.: Localization expansions I. Function of the background configurations. Commun. Math. Phys. 182, 33–82 (1996)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    Dimock, J.: The renormalization group according to Balaban—I. Small fields. Rev. Math. Phys. 25, 1330010 (2013)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsSUNY at BuffaloBuffaloUSA

Personalised recommendations