Lehmann, H.; Symanzik, K.; Zimmermann, W.; Zur Formulierung quantisierter Feldtheorien / A New Formulation of Quantized Field Theories
Nuovo Cim. 1 (1955) 205;
A new formulation of quantized field theories is proposed. Starting from some general requirements we derive a set of equations which determine the matrix-elements of field operators and the S-Matrix. These equations contain no renormalization constants, but only experimental masses and coupling parameters. The main advantage over the conventional formulation is thus the elimination of all divergent terms in the basic equations. This means that no renormalization problem arises. The formulation
is here restricted to theories which do not involve stable bound states. For simplicity we derive the equations for spin 0 particles, however the extension to other cases (e.g. quantum electrodynamics) is obvious. The solutions of the equations are discussed in a power-series expansion. They are then identical with the renormalized expressions of the conventional formulation. However, the equations set up here are not restricted to the application of perturbation theory.
Related references See also E. P. Wigner, Annals of Math. 30 (1939) 149;
M. Gell-Mann, M. L. Goldberger, and W. E. Thirring, Phys. Rev. 95 (1954) 1612;
K. Symanzik, Zeit. Naturforschung 10A (1954) 809;
W. Zimmermann, Nuovo Cim. Suppl. 11 (1954) 43;
W. Zimmermann, Nuovo Cim. 11 (1954) 416;
G. Källen, Helv. Phys. Acta 25 (1952) 417;
Beginnings of the axiomatic field theory of the S-matrix.