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Introduction to symmetry analysis by Brian Cantwell in 2002

1. Introduction to symmetry

1.4 The principle of covariance

  • Definition 1.2 (The principle ofcovariance). The equations thatgovern a phys* ical law must retain the same appearance under certain group transformations of the variables that appear in the equations. This principle incorporates two somewhat distinct ideas.

    • (i) Coordinate independence – Physical phenomena must be governed by laws that do not depend on the coordinate system used to describe the phenomena.
    • (ii) Dimensional homogeneity – Physical phenomena must be described by laws that do not depend on the unit ofmeasure applied to the dimensions ofthe variables that describe the phenomena.
  • (i) Coordinate independence – Physical phenomena must be governed by laws that do not depend on the coordinate system used to describe the phenomena.
  • (ii) Dimensional homogeneity – Physical phenomena must be described by laws that do not depend on the unit ofmeasure applied to the dimensions ofthe variables that describe the phenomena.