The conclusive volume of the Brandeis University Summer Institute lecture series of 1970 on theories of interacting elementary particles consisting of five sets of lectures. The five sets of lectures are as follows: Rudolph Haag (II. Institut fur Theoretische Physik der Universitat Hamburg) on "Observables and Fields": introduction; axiomatic quantum field theory in various formulations; structure of superselection rules; charge quantum numbers; statistics; parastatistics.Maurice Jacob (CERN, European Organization for Nuclear Research) on "Regge Models and Duality": introduction; duality in a semi-local way; duality and unitary symmetry; dual models for meson-meson scattering; dual models for production proceses; from dual models to a dual theory.Henry Primakoff (University of Pennsylvania) on "Weak Interactions": introduction; lepton conversation and the implications of a possible lepton non-conversation; first-order and second-order weak collision processes; "abnormalities in the weak currents and how to discover them; conclusion.Michael C. Reed (Princeton University)on "The GNS Construction -- A Pedagogical Example": infinite tensor products of Hilbert spaces; the canonical anti-commutation relations; the example; the example -- via the GNS construction.Bruno Zumino (CERN, European Organization for Nuclear Research) on "Effective Lagrangians and Broken Symmetries": Introduction; effective action and phenomenological fields; Ward identities and the effective action; Goldstone's theorem; non-linear realizations; massive Yang-Mills fields as phenomenological fields; broken scale invariance; the fifteen parameter conformal group and the Weyl transformations; conversion identities and trace identities; invariant actions; SU(3)xSU(3)and conformalinvariance; strong gravitation; concluding remarks.

The first volume of the Brandeis University Summer Institute lecture series of 1970 on theories of interacting elementary particles, consisting of four sets of lectures. Every summer since 1959 Brandeis University has conducted a lecture series centered on various areas of theoretical physics. The areas are sufficiently broad to interest a large number of physicists and the lecturers are among the original explorers of these areas. The 1970 lectures, presented in two volumes, are on theories of interacting elementary particles. The four lecturers of Volume 1, and the range of the topics they cover, are as follows: Stephen L. Adler (Institute for Advanced Study) on "Perturbation Theory Anomalies": introduction and review of perturbation theory; the VVA triangle anomaly; absence of radiative corrections; generalizations of our results; connection between Ward identity anomalies and commutator (Bjorken-limit) anomalies; applications of the Bjorken limit; and breakdown of the Bjorken limit in perturbation theory. Stanley Mandelstam (University of California at Berkeley) on "Dynamical Applications of the Veneziano formula for the four-point scalar amplitude; factorization; the operator formalism; Veneziano-type quark models; and higher-order Feynman-like diagrams. Steven Weinberg (Massachusetts Institute of Technology) on "Dynamic and Algebraic Symmetries": Introduction; hadron electrodynamics; local symmetries; and chirality. Wolfhart Zimmermann (New York University) on "Local Operator Products and Renormalization in Quantum Field Theory": introduction; renormalization; operator product expansions; and local field equations. The second volume contains lectures by Rudolf Haag on observables and fields, by Maurice Jacob on duality, by Michael Reed on non-Fock representations, and by Bruno Zumino on effective Lagrangians and broken symmetries.