By P. M. Cohn
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Additional resources for Algebra. Volume 1. Second Edition
All theories contain an element of idealization and, therefore, a modelling element. In celestial mechanics, the planets are ideally hard spheres or, more often, even material pOints, whereas in fact this is not the case. All theories, even the best ones, are model theories; it is a question of the degree of accuracy. But in any case, in OED theory, it is possible to calculate observable quantities but in OeD, nobody has succeeded in obtaining from the theory the ordinary hadrons. PHYS. There are reasonable conjectures about how they could be obtained.
Thus there came about the idea that P and N are two states of one and the same particle and the nuclear forces need to be written in the isotopically invariant form. The well-known spin matrices for particles with spin 1/2 were already being used, and by analogy, interactions with isospin matrices 't were introduced. MATH. I think that you are oversimplifying the whole story to some extent. As I recall, the two states of the nucleon and the 't operators appeared earlier. They were already used in Fermi's article on the theory of ~-decay in 1934 in which he makes reference to Heisenberg's work of 1932 .
Officially this is called "second quantization", "functional integration", "perturbation theory". The bits of mathematics that I am in a pOSition to glean from the text books and preprints promise something beautiful and important, but do not form part of some definitive picture. OeD does not have the power to explain the fundamental phenomenon in strong interactions, namely, colour confinement, but forces us to reject one of the basic dogmas of OFT, namely the completeness of the space of free states of 38 CHAPTER 1 particles.
Algebra. Volume 1. Second Edition by P. M. Cohn