Covariance means form invariance, i.e. the form of a physical law is unchanged (invariant) with respect to transformations of reference systems. Covariance can be distinguished from ► invariance which refers to quantities and objects [2]. The co-variant formulation of laws implies that the form of laws is independent of the state of motion in a reference system that an observer takes. In that sense, all fundamental laws of classical and relativistic physics are covariant [3,4]. According to the definition of covariance, the gauge principle (► gauge symmetry; symmetry) can also be considered a principle of gauge covariance [5].
In quantum mechanics, measurable quantities (eigenvalues, probabilities, ex-pectation values) are invariants (► invariance) with respect to unitary transforma-tions (► symmetry). But the form of laws changes in a ► Heisenberg picture or ► Schrödinger picture. The fundamental laws of quantum mechanics can also be formulated in a covariant form with respect to arbitrary unitary transformations [1].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Primary Literature
E. Schmutzer: Eine neue Grundlegung der Quantenmechanik. Nova Acta Leopoldina 44(8), 79–158 (1976)
Secondary Literature
F. Friedman: Foundations of Space-Time Theories (Princeton University Press, Princeton, 1983)
K. Mainzer: Symmetrien der Natur (De Gruyter, Berlin, 1988; English trans. Symmetries of Nature, De Gruyter, New York, 1996)
K. Mainzer: Symmetry and Complexity. The Spirit and Beauty of Nonlinear Science (World Scientific, Singapore, 2005)
T.Y. Cao: Gauge Theory and the Geometrization of Fundamental Physics. In: H.R. Brown, R. Harré (eds.): Philosophical Foundations of Quantum Field Theory (Clarendon Press, Oxford, 1988)
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Mainzer, K. (2009). Covariance. 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_41
Download citation
DOI: https://doi.org/10.1007/978-3-540-70626-7_41
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)