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  • Print publication year: 2010
  • Online publication date: December 2010

3 - Sum rules


Current algebra, as a hypothesis about hadron physics, offers a set of algebraic relations relating one physically measurable quantity to another, although it cannot be used to calculate any from first principles. Presumably, the assumed validity of a hypothesis should first be tested before it can be accepted and used for further explorations. However, any exploration of the implications or applications of the hypothesis, within the general framework of hypothetic-deductive methodology, if its results can be checked with experiments, functions as a test.

The test of current algebra, however, requires delicate analyses of hadronic processes and effective techniques for identifying relevant measurable quantities in a justifiable way. For this reason, there was no rapid progress in current algebra until Sergio Fubini and Giuseppe Furlan (1965) suggested certain techniques that can be used, beyond its initial applications, to derive various sum rules from current algebra, which can be compared with experimental data. The importance of the sum rules thus derived, however, goes beyond testing the current algebra hypothesis. In fact, they had provided the first conceptual means for probing the constitution and internal structure of hadrons, and thus had created a new situation in hadron physics and opened a new direction for the hadron physics community to move, as we shall see in the ensuing sections and chapters.