An Axiomatic Sufficient Framework for Fermionic Topological Solitons

This paper develops a set of clear, sufficient conditions under which nonlinear field theories in (3+1) dimensions support stable topological solitons that quantize as fermions in the Finkelstein–Rubinstein sense. The framework isolates three ingredients: (i) variational existence of finite-energy minimizers in fixed topological charge; (ii) local well-posedness of the hyperbolic Cauchy problem within a quantified regime; and (iii) a topological computation showing that a (2\pi) spatial rotation represents the nontrivial loop in configuration space. Applied to the classical Skyrme model with standard boundary conditions, the axioms yield the result that odd-charge Skyrmions quantize as fermions. The work clarifies the structural requirements for FR quantization and highlights the scope and limitations of current methods.