Spin and statistics with an indefinite metric

Abstract

A theory of spin- 1 2 bosons and spin-0 fermions formulated with an indefinite metric for physical states is considered. The requirement that squares of S-matrix elements be interpretable as probabilities in the usual sense is formulated in terms of a symmetry principle as a consequence of which states with positive norms become separated from those with negative norms by a superselection law. The symmetry transformation, called metric conjugation, is induced by the metric operator and is non-local. An example of an interaction invariant under metric conjugation is shown to lead to a unitary S matrix and to a theory that admits a causal interpretation in the sense of Stueckelberg. Some consequences of the assumption that the muon is a spin- 1 2 boson are discussed. The theory then provides a physical basis for the absence of the decays μ→e+ γ, μ→3e in the sense that the conservation law which leads to these selection rules is the one required for the theory to admit a physical interpretation. The same conservation law forbids muon pair production.