Towards a two-field theory of elementary particles
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It is shown why the symmetry principle between the baryon triplet (Λnp) and lepton triplet (μ eν) suggests a two-field theory of elementary particles. One massless spinor field is used to describe the nucleons and light leptons and a second spinor field with finite bare mass the « strange » particles Λ andμ. The two-field model resembles the theories of Heisenberg and Nambu in several respects but there are also important differences which are spelled out.
Si mostra come il principio di simmetria tra il tripletto di barioni (Λnp) e il tripletto di leptoni (μeν) suggerisca per le particelle elementari una teoria a due campi. Si usa un campo spinoriale per descrivere i nucleoni e i leptoni leggeri e un secondo campo spinoriale con massa nuda finita per descrivere le particelle « strane » Λ eμ. Sotto molti aspetti il modello a due campi è simile alla teoria di Heisenberg e di Nambu ma esistono anche notevoli differenze che si mettono in evidenza.
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- (7).Y. Nambu andG. Jona-Lasinio: preprint (University of Chicago); this will be referred to as the Nambu theory. Cfr. alsoJ. Goldstone: CERN preprint.Google Scholar
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- (14).The reasons are different for the two authors;Nambu discards them=0 solution since he believes that it is unstable on two counts: 1) the analogy with superconductivity (where the superconducting state is stable and the normal state is not) and 2) on the basis of a calculation of the difference between the divergent zero-point energies. However, neither argument is conclusive: 1) the normal state becomes as stable as the superconducting state in the limit of infinite volume of the superconductor which corresponds more closely to the elementary particle case with its infinite number of degrees of freedom and hence there is no reason why two solutions should not be equally stable in two orthogonal Hilbert spaces and 2) the meaning of the divergent zero-point energy is unclear at the present stage of quantum field theory. On the other hand, Heisenberg effectively discards them=0 solution since he wishes to describe the leptons by means of the « scale » transformation. Besides, in the Heisenberg theory, the propagator function is chosen in such a way that it is zero form=0 and therefore it is self-consistent to discard them=0 solution.Google Scholar
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