| Symmetry and Symmetry Breaking (Stanford Encyclopedia of Philosophy) |

| | The first explicit study of the **invariance** properties of equations in **physics** is connected with the introduction, in the first half of the nineteenth century, of the transformational approach to the problem of motion in the framework of analytical mechanics. |

| | The diffeomorphism freedom of GTR, i.e., the **invariance** of the form of the laws under transformations of the coordinates depending smoothly on arbitrary functions of space and time, is a “local” spacetime symmetry, in contrast to the “global” spacetime symmetries of STR (which depend instead on constant parameters). |

| | In contemporary **physics**, the best example of this role of symmetry is the classification of elementary particles by means of the irreducible representations of the fundamental **physical** symmetry groups, a result first obtained by Wigner in his famous paper of 1939 on the unitary representations of the inhomogeneous Lorentz group. |

| plato.stanford.edu /entries/symmetry-breaking (9815 words) |