Galilei Group and Galilean Invariance

Publisher Summary Galileo Galilei explicitly introduced the principle of relativity in physics. He was the first one to recognize the existence of inertial transformations, connecting various frames of reference in which the laws of physics take the same form. Starting with the recognition that the Galilean transformation laws were but an approximation to the more exact Lorentz formulas, one could distinguish the abstract principle of relativity from its concrete expressions, as various possible theories of relativity. At the same time, one could begin to see the basic role played by the relevant theory of relativity in structuring a given physical theory—Galilean relativity for classical mechanics, Einstein relativity for “relativistic” mechanics, and electromagnetism. Applications of the Galilei group are described for classical physics and for quantum physics. A “super-Galilei group” has been defined in relation to non-relativistic cosmology. This is a sixteen-parameter group acting on the five-dimensional manifold of space-time and gravitational potential.

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