Nontopological Methods for Determining Topological Charge for Bosons and Fermions in Flat Spacetime

An alternative method to the topological instanton solution for deriving an expression for the topological charge is presented. This alternative method involves the use of relativistic quantum field theory and covariant electrodynamics. In the case of bosons, this method is consistent with the instanton solution in predicting that topological charge is quantized. But furthermore, this method led to the new results that topological charge for fermions cannot be quantized, whereas the instanton solution cannot distinguish between bosons (quantized) and fermions (not quantized). Thus the new technique produced results that were previously unobtainable. Mathematics Subject Classifications (1991): // Key words: Topological charge, Dirac quantization condition, Klein-Gordon equation