Astronomy and Astrophysics – Astrophysics
Scientific paper
Apr 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002aps..apr.i3004m&link_type=abstract
American Physical Society, April Meeting, Jointly Sponsored with the High Energy Astrophysics Division (HEAD) of the American As
Astronomy and Astrophysics
Astrophysics
Scientific paper
Concepts of symmetry in physics have had a long history, particularly if they are of a geometric or crystallographic origin, yet in classical physics they had a somewhat esoteric position. This situation changed radically when in the XX Century we passed from classical to quantum mechanics. In the former a state for a system of particles was given by a number of points in phase space and the transformation groups related with symmetries mainly gave the invariance of concepts such as energy or angular momentum. In the latter the state is characterized by a vector in Hilbert space in which the transformations had a representation. Eugene Wigner was the right man (for his mathematical ability and physical intuition) at the right place and time (Germany, in the twenties) to take full advantage of this new situation. His first interest was atomic spectroscopy (then a very active field) and the fact that its basic states were related with irreducible representation of the orthogonal group in three dimensions O(3). The German version of his book on ``Group theory and Application" published in 1931 established, as he quotes ``that almost all rules of spectroscopy follow from the symmetry of the problem". His later extension to the direct product of two or more representations led to his development of the 3-j symbol, that he explicitly derived, and his interest in the properties of 6-j, 9-j, etc. His awareness of the time inversion as an antiunitary operator, and the analysis of its combination with the unitary representations of other symmetries, proved fundamental for deriving the features of time reversed reactions from their direct behavior. His interest in space reflection and the concept of parity led to important selection rules, and was of relevance even in weak interactions where parity is not a good symmetry. His later interest in nuclear physics, solid state, elementary particles etc., was almost never without a component of the role of symmetry in these problems. The best example of this is his work on the ``Unitary representations of the inhomogeneous Lorentz group" (1939) which led later to the possible form of equations and interactions in the elementary particle field. Eugene Wigner was certainly one of the giants of XX Century physics and his contribution not only influenced the field in his time but is also likely to be fundamental in the century that will follow the centennial we are celebrating now.
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