Relativistic calculations of the Green’s functions by means of the continuous integration in the case of strong coupling

Abstract

A strong coupling theory is studied for self coupled meson field with vanishing bare mass by making use of continuous integration. Particularly, the one-particle propagator is discussed. Some remarks are made on the GOLDSTONE model.The airo of our work is to develop a method for the calculation of Green's functions from a given Lagrangeanin a Lorentz-invariant manner and in the case of strong interactions. For renormalizable cases the result should also be renormalizable. So it should be a true alternative to perturbation theory, ir coupling is strong. It seems to us very important to have sueh a method; it would be very useful for giving an answer to many problems of quantum field theory and the theory of elementary particles.We develop our method here on the simple model with the Lagrangean