Approximate symmetry and the algebra of current components

Abstract

It is our purpose to explain in this note, as well as we can, the theoretical foundations of the approximate symmetries of hadrons that have been extensively discussed lately, including the generalization of U(6) symmetry and its application to moving hadrons. A scheme (1-3] using the non-compact group U(6, 6), but not as an approximate symmetry of quantum mechanical states, has attracted wide attention; although the scheme contradicts [ 4] conservation of probability and certain experimental results, it predicts certain other quantities correctly. These correct predictions, by and large, follow from our method, which are consistent with probability conservation and involve applying symmetry operators to the states.

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