Covariance

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].

Editors and Affiliations

1. Department of Physics, The City College of New York, 138th St. & Convent Ave., New York, NY, 10031, USA

   Daniel Greenberger

2. Section for the History of Science & Technology, University of Stuttgart, Keplerstr. 17, Stuttgart, D-70174, Germany

   Klaus Hentschel

3. Department of Social Sciences and Humanities, University of Bradford, Bradford, BD7 1DP, UK

   Friedel Weinert

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