Topological Analysis of a Nonlinear Field Theory

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Abstract
This paper is concerned with a class of nonlinear field theories that exhibit conserved particlelike structures. An example of such a theory is quoted. Fields belonging to this theory are classical fields, single-valued under the action of the rotation group. It is explained how, when the theory is quantized, the quantum mechanical states which correspond to 1-particle systems in the unquantized theory may have properties similar to fermion states. In particular, it is shown that it is possible for wavefunctionals to exist which are double-valued under 2π rotations. This is the first known example in which a single-valued field theory can give rise to a quantized theory with half-odd spin properties.

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