Lochlainn O’Raifeartaigh, Fluids, and Noncommuting Fields

Lochlainn O’Raifeartaigh and his work are recalled; the connection between fluid mechanics – his last research topic – and noncommuting gauge fields is explained. O’Raifeartaigh Memorial Meeting, Dublin, Ireland, September 2002 Lochlainn O’Raifeartaigh, Fluids, and Noncommuting Fields 3 Lochlainn O’Raifeartaigh was an eminent theoretical/mathematical physicist, the most recent member of a cohort of outstanding Irish physicists that includes Hamilton, Stokes, Father Callan (the inventor of the induction coil), Fitzgerald, Walton, Synge, and others. I came to know him in the 1970s during his visits to my colleague the mathematician Irving Segal. Of course, I already knew his famous work from the 1960s, wherein he put a stop to a search for a group-theoretical combination of internal and kinematical relativistic symmetries. At that time, particle physicists were impressed by Wigner’s successful combination of spin SU(2) and isospin SU(2) into an SU(4) of nuclear physics, and they tried to find something similar for the quark model. The obvious choice was an SU(6) built from spin and Gell-Mann’s flavor SU(3), but this was a nonrelativistic construction and the search was on for a relativistic version. Various authors pointed out various difficulties with the idea, but the definitive paper was Lochlainn’s Physical Review Letter in which he proved that unacceptable mass degeneracies follow when the putative invariance group contains internal symmetries and Poincaré symmetries, mixed in a nontrivial way. This story is documented in Dyson’s collection Symmetry Groups in Nuclear and Particle Physics. Although more definitive no-go theorems were later constructed, serious research on “relativistic SU(6)” stopped with the publication of “O’Raifeartaigh’s theorem”. But the desire of physicists to combine Poincaré and internal symmetries did not stop, and this is an interesting example of how the force of physics, which derives from Nature, overcomes mathematical obstacles, which are put up by human ingenuity! Of course, I am referring to supersymmetry, which evades all no-go theorems and does combine internal with space-time symmetries through the simple expedient of mixing bosons and fermions – something that does not happen for transformations belonging to ordinary symmetry groups. Again, Lochlainn contributed decisively to this newly evolved idea. Supersymmetry still entails unacceptable mass degeneracies, between bosons and fermions. In his most-cited paper on the “O’Raifeartaigh mechanism”, he constructed simple examples in which supersymmetry is spontaneously broken, and the unwanted mass-degeneracies are removed. In later years Lochlainn wrote extensively on historical and pedagogical topics, centered on gauge theories. I recommend especially his two books: Group Structure of Gauge Theories and The Dawning of Gauge Theory, and two articles: “Gauge Theory: The Gentle Revolution” and “Gauge Theory: Historical Origins and Some Modern Developments”, the last with Straumann. These works reflect his life-long desire to teach, clarify, and explain physics intricacies, and this is also seen from the vast number of schools, symposia, and meetings to which he contributed – I counted twenty-five in the last decade. Both the research and the teaching were fittingly recognized by the Wigner medal, which he received just before he died. Lochlainn and I never collaborated on actual research, but our interests paralleled each other to a significant degree. Both he and I explored anomalies; we both wrote