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George Sudarshan, No-Go theorems and the exclusion principle

We review two areas of my work that were directly and indirectly initiated and inspired by George. One is the proofs of no-go theorems in combining the spacetime and internal symmetries in non-trivial ways and the other is how Georges firm conviction on the fundamentality of the spin-statistics theorem helped to expand the domain of applicability of the spin-statistics theorem into the arena of quarks and gluons, going far beyond the original application of the exclusion principle in atomic physics. In order to provide deeper understanding of mass differences of particles belonging to spin-degenerate multiplets, attempts have been made to see if some non-trivial way of embedding the Lorentz group and internal symmetry groups such as SU(2) and SU(3) into a larger group. When a hint of no-go theorem (that such non-trivial embedding cannot be achieved) first appeared, George went to work and led many of us, including myself, into this area of research. A series of proofs of no-go theorems by George, myself and others eventually led to the definitive proof by Lochlainn O'Raifeartaigh that came to be known as the ORaifeartaigh theorem. Lochlainn also joined George at Syracuse at the same time I went there. The second area in which George had significant influence on my work is his fervent belief in the fundamental importance of the spin-statistics relationship. First postulated by Worlfgang Pauli to explain the periodic table of elements, the relationship the exclusion principle has exceeded far beyond its original domain of validity. The relationship has been upheld across the scale molecular, atomic, and nuclear structures. What is less known is the fact the relationship continues to remain valid in scales smaller than nucleons. The spin-statistics relationship was one of the compelling reasons for Nambu and I to introduce a new set of then undiscovered degrees freedom for quarks inside nucleons. This new degrees of freedom came to be called the color charges of quarks and it led to the non-Abelian gauge field theory of the strong interactions known today as the quantum chromodynamics. Georges insight into the spin-statistics relationship was indispensable in the birth of the new theory of the strong force.