Abstract
We consider the Abelian gauge theories in which the transverse and the longitudinal photons are coupled. The unitarity relation holds because the unwanted absorptive part of the amplitude due to this coupling is canceled by the fictitious particle. It is pointed out that, by introducing the Lagrange multiplier, one can see the cancellations for all orders in perturbation expansions by looking at the equation of motion for the Lagrange multiplier. The possible implication of this on the massless Yang-Mills fields is indicated.
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