Coupled Fields :

We formulate a general theory of the strong coupling limit of renormalizable interacting quantum fields. For definiteness, our ideas are explicitly illustrated in the case of the scalar field with quartic self-coupling, the usual testing ground for new ideas in field theory. More precisely, the generating functional for connected Green's functions is explicitly constructed for this latter theory in the limit of large coupling. The problem of regulariza-tion is treated in detail. For purposes of illustration, the first two orders in the large coupling limit of the Fourier transform of the connected two point function are computed. It is found that the Fourier transform for 4-momentum p approaches its large-(p 2) limit essentially exponentially. The applicability of our approach to all renor-malizable theories is thereby made more manifest.