Charges and currents in the Thirring model

by R. F. Streater; pp 375-386 in "Physical Reality and Mathematical Description", eds. C. P. Enz and J. Mehra. D. Reidel, 1974.

ABSTRACT

We give an informal account of the recent theory of superselection rules due mainly to R. Haag, and we treat a simple model field theory from this point of view, following a paper of I. F. Wilde and the author, written in 1970. The model, similar to one studied by Skyrme in 1960, turns out to yield the Thirring model, if suitable limits are taken, as is seen by comparing the equations with the work of Dell'Antonio, Frischman and Zwanziger.

REMARKS

Our treatment of the model shows that the charges and superselection rules, and to some extent the Fermi field operator and its equations of motion, are intrinsically determined by the observables, that is the currents, of the theory.

This work was written in Feb. 1973; it shows that the excitons of the free Boson field of zero mass in 1+1 dimensions may have commutation relations other than Boson or Fermion. This construction of the Fermion from a Boson field was invented by Skyrme in 1958, and is here made rigorous. It became known as "bosonization", especially after Coleman and Mandelstam studied the case of the massive Thirring model. They were unaware of Skyrme's earlier work, and also of my series of papers, including this one.