Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-23T14:11:51.239Z Has data issue: false hasContentIssue false
  • English
  • Français

Constraining the Higgs Mechanism: Ontological Worries and the Prospects for an Algebraic Cure

Published online by Cambridge University Press:  01 January 2022

Michael Stöltzner
Get access Rights & Permissions [Opens in a new window]

Abstract

I discuss Earman's program to achieve an objective account of the Higgs mechanism within the C∗ algebraic approach to quantum field theory. Pointing to three results obtained within this approach, I argue that if one follows Earman and understands the Higgs mechanism as a constraint, it appears to be a genuine quantum phenomenon that does not simply arise through the correspondence principle. This casts further this casts doubts on the validity of the Dirac conjecture that identifies first-class constraints and gauge transformations and that provides a major motivation for both Earman's program and Struyve's demonstration that a gauge-invariant account of the Higgs mechanism can be accomplished at the classical level.

Type
Physics
Information
Philosophy of Science , Volume 79 , Issue 5 , December 2012 , pp. 930 - 941
Copyright
Copyright © The Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

†

This article has profited from numerous discussions within the interdisciplinary research group “The Epistemology of the Large Hadron Collider” that is supported by the DFG (German Research Foundation; see http://www.lhc-epistemologie.uni-wuppertal.de/).

References

Baker, David John, and Halvorson, Hans. 2011. “How Is Spontaneous Symmetry Breaking Possible?” Unpublished manuscript. http://arxiv.org/abs/1103.3227v1.Google Scholar
Buchholz, Detlev. 2008. “Quantenfeldtheorie ohne Felder: Ein alternativer Zugang.” Physik Journal 7 (8–9): 45–50.Google Scholar
Buchholz, Detlev, Doplicher, Sergio, Longo, Roberto, and Roberts, John E.. 1992. “A New Look at Goldstone's Theorem.” Reviews in Mathematical Physics, special issue, 4:49–83.CrossRefGoogle Scholar
Dirac, Paul A. M. 1955. “Gauge-Invariant Formulation of Quantum Electrodynamics.” Canadian Journal of Physics 33:650–60.CrossRefGoogle Scholar
Dirac, Paul A. M.. 1964. Lectures on Quantum Mechanics. New York: Belfer Graduate School.Google Scholar
John, Earman. 2004a. “Curie's Principle and Spontaneous Symmetry Breaking.” International Studies in the Philosophy of Science 18:173–98.Google Scholar
John, Earman. 2004b. “Laws, Symmetry, and Symmetry Breaking: Invariance, Conservation Principles, and Objectivity.” Philosophy of Science 71:1227–41.Google Scholar
Fraser, Doren. 2011. “How to Take Particle Physics Seriously: A Further Defence of Axiomatic Quantum Field Theory.” Studies in History and Philosophy of Modern Physics 42:126–35.CrossRefGoogle Scholar
Grundling, Hendrik, and Hurst, C. A.. 1985. “Algebraic Quantization of Systems with a Gauge Degeneracy.” Communications in Mathematical Physics 98:369–90.CrossRefGoogle Scholar
Grundling, Hendrik, and Hurst, C. A.. 1987. “Algebraic Structures of Degenerate Systems and the Indefinite Metric.” Journal of Mathematical Physics 28:559–72.CrossRefGoogle Scholar
Grundling, Hendrik, and Hurst, C. A.. 1988a. “A Note on Regular States and Supplementary Conditions.” Letters in Mathematical Physics 15:205–12. Errata in Letters in Mathematical Physics 17 (1989): 173–74.CrossRefGoogle Scholar
Grundling, Hendrik, and Hurst, C. A.. 1988b. “The Quantum Theory of Second Class Constraints: Kinematics.” Communications in Mathematical Physics 119:75–93.CrossRefGoogle Scholar
Grundling, Hendrik, and Hurst, C. A.. 1988c. “Systems with Outer Constraints: Gupta-Bleuler Electromagnetism as an Algebraic Field Theory.” Communications in Mathematical Physics 114:69–91.CrossRefGoogle Scholar
Halvorson, Hans. 2006. “Algebraic Quantum Field Theory.” In Handbook of the Philosophy of Physics, ed. Butterfeld, Jeremy and Earman, John, 731–922. Dordrecht: Kluwer.Google Scholar
Henneaux, Marc, and Teitelboim, Claudio. 1989. Quantization of Gauge Theories. Princeton, NJ: Princeton University Press.Google Scholar
Higgs, Peter W. 1966. “Spontaneous Symmetry Breakdown without Massless Bosons.” Physical Review 145:1156–63.CrossRefGoogle Scholar
Karaca, Koray. 2012. “The Construction of the Higgs Mechanism and the Emergence of the Electroweak Theory.” Studies in History and Philosophy of Modern Physics, forthcoming.Google Scholar
Lyre, Holger. 2008. “Does the Higgs Mechanism Exist?” International Studies in the Philosophy of Science 22:119–33.CrossRefGoogle Scholar
Lyre, Holger. 2010. “The Just-So Higgs Story: A Response to Adrian Wüthrich.” Unpublished manuscript, PhilSci Archive. http://philsci-archive.pitt.edu/id/eprint/5513.Google Scholar
Morrison, Margaret. 2003. “Spontaneous Symmetry Breaking: Theoretical Arguments and Philosophical Problems.” In Symmetries in Physics: Philosophical Reflections, ed. Brading, Katherine and Castellani, Elena, 347–63. Cambridge: Cambridge University Press.Google Scholar
Smeenk, Chris. 2006. “The Elusive Higgs Mechanism.” Philosophy of Science 73:487–99.CrossRefGoogle Scholar
Stöltzner, Michael. 1995. “Non-regular Representations in Quantum Electrodynamics.” Diploma thesis, University of Vienna.Google Scholar
Stöltzner, Michael. 2001. “Opportunistic Axiomatics: John von Neumann on the Methodology of Mathematical Physics.” In John von Neumann and the Foundations of Quantum Physics, ed. Rédei, Miklós and Stöltzner, Michael, 35–62. Dordrecht: Kluwer.CrossRefGoogle Scholar
Struyve, Ward. 2011. “Gauge Invariant Accounts of the Higgs Mechanism.” Studies in History and Philosophy of Modern Physics 42:226–36.CrossRefGoogle Scholar
Thirring, Walter, and Narnhofer, Heide. 1992. “Covariant QED without Indefinite Metric.” Reviews in Mathematical Physics, special issue, 4:197–211.CrossRefGoogle Scholar
Wallace, David. 2011. “Taking Particle Physics Seriously: A Critique of the Algebraic Approach to Quantum Field Theory.” Studies in History and Philosophy of Modern Physics 42:116–25.CrossRefGoogle Scholar
Wüthrich, Adrian. 2010. “Eating Goldstone Bosons in a Phase Transition: A Critical Review of Lyre's Analysis of the Higgs Mechanism.” Unpublished manuscript, PhilSci Archive. http://philsci-archive.pitt.edu/id/eprint/5496.Google Scholar