Gauge symmetry breaking in gauge theories—in search of clarification

  • Simon Friederich
Original paper in Philosophy of Physics


The paper investigates the spontaneous breaking of gauge symmetries in gauge theories from a philosophical angle, taking into account the fact that the notion of a spontaneously broken local gauge symmetry, though widely employed in textbook expositions of the Higgs mechanism, is not supported by our leading theoretical frameworks of gauge quantum theories. In the context of lattice gauge theory, the statement that local gauge symmetry cannot be spontaneously broken can even be made rigorous in the form of Elitzur’s theorem. Nevertheless, gauge symmetry breaking does occur in gauge quantum field theories in the form of the breaking of remnant subgroups of the original local gauge group under which the theories typically remain invariant after gauge fixing. The paper discusses the relation between these instances of symmetry breaking and phase transitions and draws some more general conclusions for the philosophical interpretation of gauge symmetries and their breaking.


Quantum field theory Gauge symmetries Symmetry breaking Phase transitions Higgs mechanism 



I would like to thank Kerry McKenzie, Robert Harlander, Dennis Lehmkuhl, Holger Lyre, Michael Kobel, Michael Krämer, Michael Stöltzner, Ward Struyve and anonymous referees who reviewed this article for many helpful comments. Furthermore, I am grateful to Jeff Greensite, Gernot Münster and Franco Strocchi for useful answers to questions I raised.


  1. Brading, K., & Castellani, E. (Eds.) (2003). Symmetries in physics: Philosophical reflections. Cambridge, UK: Cambridge University Press.Google Scholar
  2. Buchmüller, W., Fodor, Z., Hebecker, A. (1994). Gauge invariant treatment of the electroweak phase transition. Physics Letters B, 331, 131–136.CrossRefGoogle Scholar
  3. Caudy, W., & Greensite, J. (2008). Ambiguity of spontaneously broken gauge symmetry. Physical Review D, 78, 025018.CrossRefGoogle Scholar
  4. De Angelis, G.F., De Falco, D., Guerra, F. (1978). Note on the Abelian Higgs-Kibble model on a lattice: absence of spontaneous magnetization. Physical Review D, 17, 1624–28.CrossRefGoogle Scholar
  5. Earman, J. (2004). Laws, symmetry, and symmetry breaking: invariance, conservation principles, and objectivity. Philosophy of Science, 71, 1227–1242.CrossRefGoogle Scholar
  6. Elitzur, S. (1975). Impossibility of spontaneously breaking local symmetries. Physical Review D, 12, 3978–3982.CrossRefGoogle Scholar
  7. Fradkin, E., & Shenker, S.H. (1979). Phase diagrams of lattice gauge theories with Higgs fields. Physical Review D, 19, 3682–3697CrossRefGoogle Scholar
  8. Friederich, S. (2011). How to spell out the epistemic conception of quantum states. Studies in History and Philosophy of Modern Physics, 42(3), 149–157.CrossRefGoogle Scholar
  9. Fröhlich, J., Morchio, G., Strocchi, F. (1981). Higgs phenomenon without symmetry breaking order parameter. Nuclear Physics B, 190, 553–582.CrossRefGoogle Scholar
  10. Greaves, H., & Wallace, D. (2011). Empirical consequences of symmetries. Accessed 4 August 2012
  11. Greensite, J. (2011). An introduction to the confinement problem. Berlin, New York: Springer.CrossRefGoogle Scholar
  12. Healey, R. (2007). Gauging what’s real: The conceptual foundations of contemporary gauge theories. New York: Oxford University Press.CrossRefGoogle Scholar
  13. Intriligator, K., & Seiberg, N. (1996). Lectures on supersymmetric gauge theories and electric-magnetic duality. Nuclear Physics B–Proceedings Supplements, 45, 1–28.CrossRefGoogle Scholar
  14. Itzykson, C., & Drouffe, J.-M. (1989). Statistical field theory, vol. 1: From Brownian motion to renormalization and lattice gauge theory. Cambridge, UK: Cambridge University Press.Google Scholar
  15. Kajantie, K., Laine, M., Rummukainen, K., Shaposhnikov, M. (1996). Is there a hot electroweak phase transition at \(m_H \gtrsim m_W\)? Physical Review Letters, 77, 2287–2290.CrossRefGoogle Scholar
  16. Kosso, P. (2000). The epistemology of spontaneously broken symmetries. Synthese, 122, 359–376.CrossRefGoogle Scholar
  17. Leggett, A.J. (2006). Quantum liquids. London, UK: Oxford University Press.CrossRefGoogle Scholar
  18. Liu, C., & Emch, G.G. (2005). Explaining quantum spontaneous symmetry breaking. Studies in History and Philosophy of Modern Physics, 36, 137–163.CrossRefGoogle Scholar
  19. Lyre, H. (2004). Holism and structuralism in U(1) gauge theory. Studies in History and Philosophy of Modern Physics, 35, 643–670.CrossRefGoogle Scholar
  20. Lyre, H. (2008). Does the Higgs mechanism exist? International Studies in the Philosophy of Science, 22, 119–133.CrossRefGoogle Scholar
  21. Morrison, M. (2003). Spontaneous symmetry breaking: Theoretical arguments and philosophical problems. In K. Brading, & E. Castellani (Eds.), Symmetries in physics: Philosophical reflections (pp. 347–63). Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
  22. Münster, G., & Walzl, M. (2000). Lattice gauge theory—a short primer, lectures given at the PSI Zuoz summer school 2000. Accessed 4 August 2012
  23. Noether, E. (1918). Invariante Variationsprobleme. Nachrichten der königlichen Gesellschaft der Wissenschaften zu Gö ttingen, Mathematisch-physikalische Klasse (Vol. 2, pp. 235–57). English translation by M.A. Tavel. Accessed 4 August 2012
  24. Redhead, M. (2002). The interpretation of gauge symmetry. In M. Kuhlmann, H. Lyre, H. Wayne (Eds.), Ontological aspects of quantum field theory. Singapore: World Scientific.Google Scholar
  25. Ruetsche, L. (2011). Interpreting quantum theories. London, UK: Oxford University Press.CrossRefGoogle Scholar
  26. Sewell, G.L. (1986). Quantum theory of collective phenomena. Oxford: Clarendon Press.Google Scholar
  27. Smeenk, C. (2006). The elusive Higgs mechanism. Philosophy of Science, 73, 487–499.CrossRefGoogle Scholar
  28. Strocchi, F. (1985). Elements of quantum mechanics of infinite systems. Singapore: World Scientific.CrossRefGoogle Scholar
  29. Strocchi, F. (2008). Symmetry breaking (2nd Edn.). Berlin, Heidelberg: Springer.CrossRefGoogle Scholar
  30. Struyve, W. (2010). Pilot-wave theory and quantum fields. Reports on Progress in Physics, 73, 106001.CrossRefGoogle Scholar
  31. Struyve, W. (2011). Gauge invariant accounts of the Higgs mechanism. Studies in History and Philosophy of Modern Physics, 42, 226–236.CrossRefGoogle Scholar
  32. ’t Hooft, G. (2007). The conceptual basis of quantum field theory. In J. Butterfield, & J. Earman (Eds.), Philosophy of physics. Amsterdam: Elsevier.Google Scholar
  33. Weinberg, S. (1974). Gauge and global symmetry at high temperature. Physical Review D, 9, 3357–3378.CrossRefGoogle Scholar
  34. Wegner, F. (1971). Duality in generalized Ising models and phase transitions without local order parameter. Journal of Mathematical Physics, 12, 2259–2272.CrossRefGoogle Scholar
  35. Wilson, K. (1974). Confinement of quarks. Physical Review D, 10, 2445–2459.CrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media B.V. 2012

Authors and Affiliations

  1. 1.Universität Wuppertal, Fachbereich C – Mathematik und NaturwissenschaftenWuppertalGermany

Personalised recommendations