A graphical method for finding possible quantizable free-field theories for higher spin

Abstract

Graphs associated with the Gel'fand-Yaglom equations for arbitrary spin are used in a simple method to find the number of conditions which a good quantizable free-field theory must satisfy. The number of conditions is seen to be simply related to the line independence numbers of the s block subgraphs of the theory. This provides a rough guide as to whether a particular theory is possibly quantizable. Some examples are given. Also a general result is given which enables quick elimination of a range of 'bad' theories by visual examination of their graphs.