NEGATIVE METRIC AND UNITARITY OF S-MATRIX

It is shown that the introduction of a negative metric in quantum mechanics can lead to a unitary S-matrix, provided that all stable particle states are of positive square length. Such a possibility can be used to remove divergence difficulties in physics, while maintaining unitarity and relativistic invariance. For example, to the zeroth order of e2, the usual photon propagator may be replaced by (q2)-1 - (q2 + m2)-1, and to the zeroth order of the weak interaction constant G, the intermediate boson W± propagator may be given simply by δμν(q2 + m2)-1, assuming that m is not too small. The general theoretical implications of such a theory with negative metric, but unitary S-matrix, are analyzed. Its various experimental consequences are discussed. Explicit examples are given for some soluble models. © 1969.