SOME PROPERTIES OF AMPLITUDES AT MULTIBOSON THRESHOLDS IN SPONTANEOUSLY BROKEN SCALAR THEORY

It is shown that in a lambdaphi4 theory of one real scalar field with spontaneous breaking of symmetry a calculation of the amplitudes of pr oduction by a virtual field phi of n on-mass-shell bosons all being ex actly at rest is equivalent in any order of the loop expansion to a Eu clidean-space calculation of the mean field of a kink-type configurati on. Using this equivalence it is found that all the 1 --> n amplitudes have no absorptive part at the thresholds to any order of perturbatio n theory. This implies nontrivial relations between multiboson thresho ld production amplitudes. In particular, the on-mass-shell amplitude o f the process 2 --> 3 should vanish at the threshold in all loops. It is also shown that the factor n ! in the 1 --> n amplitudes at the thr eshold is not eliminated by loop effects.