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Lectures on Current Algebra and Its Applications CURRENT ALGEBRA AND PCAC S. B. Treiman I. INTRODUCTION The basic ideas for the subject of current algebra were introduced by Gell-Mann1 as long ago as 1961. But the development proceeded slowly for several years, until 1965, when Fubini and Furlan2 suggested the appropriate techniques for practical applications and Adler3 and Weisberger4 derived their remarkable formula relating β decay parameters to pion- nucleon scattering quantities. This inaugurated the golden age and the literature soon reflected

CURRENT ALGEBRA AND PCAC+ Sam B. Treiman Joseph Henry Laboratories Princeton University Princeton, New Jersey, 08544, USA These lecture notes were prepared in 1970 and first appeared in Lectures on Current Algebra and Its Applications, by S. B. Treiman, R. Jackiw and D. J. Gross (Princeton University Press, Princeton, N. J., 1972). Much has of course transpired since then, even in the 'classic' applications of PCAC and current algebra. For example, it's good to report that the prediction embodied in Eq. (4.11) is now confirmed experimentally to about 5

GLOBAL ASPECTS OF CURRENT ALGEBRAt * Edward Witten Joseph Henry Laboratories Princeton University Princeton, New Jersey 08544, USA ^ Reprinted with pennission from Nuclear Physics B223 (1983) 422-432. *This work was supported in part by NSF Grant PHY80-19754. A new mathematical framework for the Wess-Zumino chiral effective action is described. It is shown that this action obeys an a priori quantization law, analogous to Dirac's quantization of magnetic change. It incorporates in current algebra both perturbative and non-perturbative anomalies. The

CURRENT ALGEBRA, BARYONS, AND QUARK CONFINEMENTt * Edward Witten Joseph Henry Laboratories Princeton University Princeton, New Jersey 08544, USA ^ Reprinted with permission from Nuclear Physics B223 (1983) 433-444. *This work was supported in part by National Science Foundation under Grant No. PHY80-19754. It is shown that ordinary baryons can be understood as solitons in current algebra effective lagrangians. The formation of color flux tubes can also be seen in current algebra, under certain conditions. The idea that in some sense the ordinary

CHAPTER 7 CURRENT ALGEBRA AND SUM RULES In the last chapter we were concerned with part icles and resonances as multiplets (that i s , b a s e s of representations) of symmetry groups SU2, SU3, or SU6 and with their interactions as approximately invariant under SU2, SU3, or SU6. However these symmetries may also play a part in elementary particle physics not as a group, but as an algebra of equal- time commutations of currents (Gell-Mann, 1962). When one sandwiches such a relation between s ta te vectors, and inserts a complete sum over s t a t e s

FIELD THEORETIC INVESTIGATIONS IN CURRENT ALGEBRAt Roman Jackiw Center for Theoretical Physics Laboratory for Nuclear Science and Department of Physics Massachusetts Institute of Technology Cambridge, MA 02139, USA + This contribution first appeared in Lectures on Current Algebra and Its Applications, by S. B. Treiman, R. Jackiw and D. J. Gross (Princeton University Press, Princeton, N. J., 1972). 1. Introduction The techniques of current algebra have been developed to circumvent two difficulties which hamper progress in particle physics. These are

FIELD THEORETIC INVESTIGATIONS IN CURRENT ALGEBRA Roman Jackiw I. INTRODUCTION The techniques of current algebra have been developed to circumvent two difficulties which hamper progress in particle physics. These are (1) a lack of knowledge of the precise laws which govern elementary processes, other than electromagnetism; (2) an inability of solving any of the realistic models which have been proposed to explain dynamics. It was in this context that Gell-Mann,1 in a brilliant induction from non- relativistic quantum mechanics, proposed his now famous