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Peter Morgan said:You're absolutely right that I have eschewed Hamiltonian and Lagrangian methods as a starting point,
Quantum theory regards all elementary particles as 'point-like' objects without providing a clear definition for the term. Composite fermions and their decay products are referred to as 'two dimensional' objects. As far as the structure of the particles are concerned the theory is not transferable to a three dimensional frame (See chapter 5 of 'Composite Fermions' by Jainendra K Jain). Hence, in order to describe particles in their natural (three dimensional) state; it is, of course; necessary to abandon the starting points of two dimensional theories (i.e. Hamiltonian and Lagrangian).
The cross over between two and three dimensional theories occurs on the radius that is common to both two and three dimensional structures in the form of a 'linear vacuum force'. Three dimensional theory is classical physics, Quantum theory is mathematical prediction.