Critical questions concerning a statistical approach to the hadron mass spectrum

The authors study the problem of the hadron mass spectrum starting from an S-matrix which is explicitly considered as a unitary operator. Making use of the additional property that the connected part T/sub c/ is a compact operator, they discuss the approximation of T/sub c/ by resonances. The connection with statistics is made by using the Bernstein-Dashen-Ma formalism together with a bootstrap assumption. Although the approach remains open, it allows a critical discussion of subtle issues concerning both the Hagedorn and the dual theories. (9 refs).