Gauge symmetries characterize a class of physical theories, so-called gauge theories or gauge field theories, based on the requirement of the invariance under a group of transformations, so-called gauge transformations, which occur in a theory's framework if the theory comprises more variables than there are physically independent degrees of freedom. Gauge ► symmetry was firstly acknowledged in Maxwell's electrodynamics, where the vector potential shows a freedom of transformation in the sense that it is not uniquely determined by the Maxwell field equations, but only up to adding the derivative of a scalar function. Since all three fundamental quantum field theoretic interactions as well as gravity can be reconstructed within a gauge theoretic framework, gauge field theories represent the backbone of modern physics today, that is, the physics of the Standard Model and beyond. ► Quantum field theory; particle physics.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Primary Literature
J. L. Anderson: Principles of Relativity Physics. Academic, New York (1967).
S. Y. Auyang: How is Quantum Field Theory Possible? Oxford University Press, New York (1995).
G. Belot: Understanding Electromagnetism. The British Journal for the Philosophy of Science. 49: 531–55 (1998).
K. Brading, H. R. Brown: Are Gauge Symmetry Transformations Observable? The British Journal for the Philosophy of Science. 55 (4): 645–65 (2004).
H. R. Brown: Aspects of Objectivity in Quantum Mechanics. In J. Butterfield, Pagonis, C., editors. From Physics to Philosophy. Cambridge University Press, Cambridge (1999).
Y. M. Cho: Einstein Lagrangian as the translational Yang-Mills Lagrangian. Physical Review. D 14 (10): 2521–525 (1976).
J. Earman: Gauge Matters. Philosophy of Science. 69 (3), Suppl.: S209–S220 (2002).
J. Earman: Tracking Down Gauge: An Ode to the Constrained Hamiltonian Formalism. In: K. Brading, E. Castellani, editors. Symmetries in Physics: Philosophical Reflections. Cambridge University Press, Cambridge (2003).
D. Giulini: Remarks on the Notions of General Covariance and Background Independence. In: E. Seiler, I.-O. Stamatescu, editors. Approaches to Fundamental Physics. Springer, Berlin (2007).
K. Hayashi, T. Shirafuji: New General Relativity. Physical Review. D 19 (12): 3524–553 (1979).
R. Healey: On the Reality of Gauge Potentials. Philosophy of Science. 68 (4): 432–55 (2001).
R. Healey: Gauge Theories and Holisms. Studies in History and Philosophy of Modern Physics. 35 (4): 619–42 (2004).
R. Healey: Gauging What's Real. Oxford University Press, New York (2007).
F. W. Hehl, J. D. McCrea, E. W. Mielke, Y. Ne'eman: Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance. Physics Reports. 258: 1–171 (1995).
D. Ivanenko, G. Sardanashvily: The Gauge Treatment of Gravity. Physics Reports. 94 (1): 1–45 (1983).
C. Liu: Gauge Gravity and the Unification of Natural Forces. International Studies in the Philosophy of Science. 17 (2): 143–59 (2003).
H. Lyre: The Principles of Gauging. Philosophy of Science. 68 (3) Suppl.: S371–S381 (2001).
H. Lyre: Holism and Structuralism in U(1) Gauge Theory. Studies in History and Philosophy of Modern Physics. 35 (4): 643–70 (2004).
H. Lyre, T. O. Eynck: Curve It, Gauge It, or Leave It? Underdetermination in Gravitational Theories. Journal for General Philosophy of Science. 34 (2): 277–303 (2003).
C. Martin: Gauge Principles, Gauge Arguments and the Logic of Nature. Philosophy of Science. 69 (3), Suppl.: S221–S234 (2002).
J. Mattingly: Which Gauge Matters. Studies in History and Philosophy of Modern Physics. 37 (2): 243–62 (2006).
J. M. Nester: Is there Really a Problem with the Teleparallel Theory? Classical and Quantum Gravity. 5: 1003–010 (1988).
A. Nounou: A Fourth Way to the Aharonov-Bohm Effect. In: K. Brading, E. Castellani, editors. Symmetries in Physics: Philosophical Reflections. Cambridge University Press, Cambridge (2003).
M. Redhead: The Interpretation of Gauge Symmetry. In: M. Kuhlmann, H. Lyre, A. Wayne, editors. Ontological Aspects of Quantum Field Theory. World Scientific, Singapore (2002).
P. Teller: The Gauge Argument. Philosophy of Science. 67 (3), Suppl.: S466–S481 (2000).
R. Utiyama: Invariant Theoretical Interpretation of Interaction. Physical Review. 101 (5): 1597–1607 (1956).
T. T. Wu, C. N. Yang: Concept of Nonintegrable Phase Factors and Global Formulation of Gauge Fields. Physical Review. D 12 (12): 3845–857 (1975).
C. N. Yang: Integral Formalism for Gauge Fields. Physical Review Letters. 33 (7): 445–447 (1974).
H. Weyl: Gravitation und Elektrizität. Sitzungsberichte der Preuβischen Akademie der Wissenschaften. p. 465–480 (1918).
Secondary Literature
T.-P. Cheng, L.-F. Li: Gauge Theory of Elementary Particle Physics: Problems and Solutions. Oxford University Press, New York (2000).
M. Göckeler, T. Schücker: Differential Geometry, Gauge Theories and Gravity. Cambridge University Press, Cambridge (1987).
R. Gambini, J. Pullin: Loops, Knots, Gauge Theories and Quantum Gravity. Cambridge University Press, Cambridge (1996).
M. Henneaux, C. Teitelboim: Quantization of Gauge Systems. Princeton University Press, Princeton (1992).
M. Nakahara: Geometry, Topology and Physics. IOP Publishing, Bristol (1990).
L. H. Ryder: Quantum Field Theory. Cambridge University Press, Cambridge (1985, 21996).
T. Y. Cao: Conceptual Developments of 20th Century Field Theories. Cambridge University Press, Cambridge (1997).
L. O'Raifeartaigh: The Dawning of Gauge Theory. Princeton University Press, Princeton (1995).
L. O'Raifeartaigh, N. Straumann: Gauge Theory: Historical Origins and Some Modern Developments. Reviews of Modern Physics. 72 (1): 1–23 (2000).
J. C. Taylor: Gauge Theories in the Twentieth Century. World Scientific, Singapore (2001).
V. P. Vizgin: Unified Field Theories. Birkhäuser, Basel (1994).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Lyre, H. (2009). Gauge Symmetry. In: Greenberger, D., Hentschel, K., Weinert, F. (eds) Compendium of Quantum Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70626-7_76
Download citation
DOI: https://doi.org/10.1007/978-3-540-70626-7_76
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70622-9
Online ISBN: 978-3-540-70626-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)