We propose an extension of the old, fairly successful, phenomenological prescription for adding spin-1 fields to the chiral Lagrangian of pseudoscalar mesons to the case where the Wess-Zumino term is present. This leads to the possibility of describing within the effective-Lagrangian framework a whole class of "unnatural-parity" hadronic reactions. In particular, we study the wellknown (pure hadronic) w + 3 a and (radiative) w-+@y processes, and find good agreement with experiment, comparable to that for any of the current-algebra "theorems." The construction of the Lagrangian is seen to involve subtle theoretical issues. We are led to examine in more detail Witten's "trial-and-error" gauging of the Wess-Zumino term and note that the Bardeen form of the anomaly seems more suitable than the left-right-symmetric form for constructing an effective model with phenomenological spin-1 fields.

We implement the concept of Wilson renormalization in the context of simple quantum-mechanical systems. The attractive inverse square potential leads to a 0 function with a nontrivial ultraviolet stable fixed point and the Hulthen potential exhibits both ultraviolet and infrared stable fixed points. We also discuss the implementation of the Wilson scheme in the broader context of one-dimensional potential problems. The possibility of an analogue of Zamolodchikov's C function in these systems is also discussed.PACS number(s1: 03.65.Ca

A nonlocal and nonlinear theory of hadrons, equivalent to the color singlet sector two dimensional QCD, is constructed. The phase space space of this theory is an infinite dimensional Grassmannian. The baryon number of QCD corresponds to a topological invariant ('virtual rank') of the Grassmannian. It is shown that the hadron theory has topological solitons corresponding to the baryons of QCD.plays the role ofh in this theory; N c must be an integer for topological reasons. We also describe the quantization of a toy model with a finite dimensional Grassmannian as the phase space. In an appendix, we show that the usual Hartree-Fock theory of atomic and condensed matter physics has a natural formulation in terms of infinite dimensional Grassmannians.

for helpful discussions and for his hospitality at Bell Laboratories, where this work was begun. The support of the National Science Foundation is also acknowledged.

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