Gauge symmetry breaking in gauge theories—in search of clarification
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.
KeywordsQuantum 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.
- Brading, K., & Castellani, E. (Eds.) (2003). Symmetries in physics: Philosophical reflections. Cambridge, UK: Cambridge University Press.Google Scholar
- Greaves, H., & Wallace, D. (2011). Empirical consequences of symmetries. philsci-archive.pitt.edu/8906. Accessed 4 August 2012
- 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
- Münster, G., & Walzl, M. (2000). Lattice gauge theory—a short primer, lectures given at the PSI Zuoz summer school 2000. http://arxiv.org/abs/hep-lat/0012005. Accessed 4 August 2012
- 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. http://arxiv.org/abs/physics/0503066v1. Accessed 4 August 2012
- 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
- Sewell, G.L. (1986). Quantum theory of collective phenomena. Oxford: Clarendon Press.Google Scholar
- ’t Hooft, G. (2007). The conceptual basis of quantum field theory. In J. Butterfield, & J. Earman (Eds.), Philosophy of physics. Amsterdam: Elsevier.Google Scholar