Yasuhisa Katayama

The meson-nucleon coupling constants in Heisenbergs nonlinear field theory

SummaryThe coupling constants of π and η mesons with nucléons have been calculated within the framework of Heisenberg’s nonlinear field theory. The calculations have been carried out by rising a newiteration procedure. The pseudoscalar coupling constants turn out to be independent of the constantl occurring in the fundamental equation and they are also rather insensitive to the meson-nucleon mass ratios. The numerical values of η-nucleon and π-nucleon coupling constants turn out to be I) 8.07 and 12.20, respectively, if we use the values ofxη/x. andxπ/x which follow from the theory, and II) 11.10 and 12.5, respectively, if the empirical mass ratios are used.RiassuntoSi sono calcolate le costanti d’accoppiamento dei mesoni π ed ρ coi nucleoni entro il quadro della teoria non lineare di campo di Heisenberg. I calcoli sono stati eseguiti usando un nuovo procedimento di iterazione. Le costanti di accoppiamento pseudoscalari risultano indipendenti dalla costantel che compare nell’equazione fondamentale e sono anche relativamente insensibili ai rapporti di massa mesone-nucleone. I valori numerici delle costanti di accoppiamento η-nucleone e π-nucleone risultano essere I) 8.07 e 12.20, rispettivamente se usiamo i valorixη/x exπ/x che discendono dalla teoria, e II) 11.10 e 12.5, rispettivamente, se si usano i rapporti di massa empirici.

Over-all space-time description and third quantization

SummaryIn order to reformulate quantum field theory from the over-all space-time point of view, we take up the Feynman amplitudes constructed by the second quantized operators. In treating these Feynman amplitudes, the third quantized operators which create or annihilate the second quantized operators are introduced. These third quantized operators are embedded in a new Hilbert space and operate upon the state vectors in this space. The connection between this formulation and the usual second quantized theory is investigated. It is shown that our formalism is equivalent to Coester’s theory. Finally, employing the third quantization formalism, we discuss a possibility of further extension of the over-all space-time description.RiassuntoPer riformulare la teoria quantistica del campo dal punto di vista dello spazio- tempo generale, prendiamo le ampiezze di Feynman costruite per mezzo degli operatori di seconda quantizzazione. Trattando queste ampiezze di Feynman, si introducono gli operatori di terza quantizzazione che creano e distruggono gli operatori di seconda quantizzazione. Questi operatori di terza quantizzazione giacciono in un nuovo spazio hilbertiano e operano sui vettori di stato in questo spazio. Si esamina la connessione tra questa formulazione e la consueta teoria della seconda quantizzazione. Si dimostra che questo formalismo è equivalente alla teoria di Coester. Finalmente, servendosi del formalismo della terza quantizzazione, si discute la possibilità di un’ulteriore estensione della descrizione per mezzo dello spazio-tempo generale.

An Approach to the Unified Theory of Elementary Particles

A model for elementary particles based on relativistic rotators is considered as a promising approach to a unified theory.

Chapter 3. On the Structure of Lepton

The phenomenological and logical problems for the lepton structure are considered. The investigations are mainly concentrated on the difference between electron and muon, through the weak phenomena and also the electromagnetic phenomena. The remarkable mass difference between both particles is discussed from the standpoint of field theory. Finally a tentative scheme of the interrelation in the lepton family is proposed.

GRAVITATIONAL FIELD IN THE UNIFIED SPINOR FIELD THEORY.

The possible existence of the gravitational field within the framework of the unified spinor field theory is examined. Though the nonlinear term in the theory might be mainly responsible for hadronic processes, it could also be a source for the realization of the gravi· tational field as well as the electromagnetic field. A conjecture is made for the introduction of the neutrino with nonzero mass as a clue to the gravitational field just as the charged lepton is to the electromagnetic field. A series of crossed ladder diagrams is taken for the scattering amplitude between baryons to have a coupling constant given by the residue of a spin 2 pole with zero mass. An estimate with a special approximation gives GM2;;;:;.2TC(v/M) for the empirical value 5.9·10·89, where M and v denote the baryon and the neutrino mass respectively. Our result gives GM 2;;;:;.0.6·10-89 near the upper bound of the empirical.mass of the beta-neutrino, 200 eV. The existence of a scalar gravitational field with small mass is not allowed in our considerations.

MASS FORMULA FOR RESONANCE STATES

A formula is given relating the mass of a resonance particle to its angular momentum, isospin, baryon number, and strangeness. The formula is combined with eertatn selection rules in order to analyze the masses of groups of particles having a given angular momentum. (T.F.H.)

New Approach to the Strangeness Changing Weak Interaction

The six-body Fermi coupling description of the strangeness changing weak interaction is generalized and results from this approach are analyzed. Several tests of the sixbody coupling are also presented. (C.E.S.)

A Theory of Weak Interaction Based on a Rotator Model

A theory of weak interactions of elementary particles based on a relativistic rotator model described by the space-time point and two associated rotating frames is presented. (C.E.S.)

Intermediary Fields Based on the Lack of the Self-Current Weak Interaction

A concrete model of intermediary fields based on the lack of neutral leptonic current and self-current couplings is presented. It is assumed that all primary weak interactions are realized only by the nonstrange particles but that their coupling fields are different. The lack of all self-current couplings together with the universality of coupling constants requires fields with positive and negative metric in Hilbert space. These requirements yield a simple model that can be interpreted as the intermediary field that causes the strangeness changing weak interactions.

Chapter 4. On the Neutrino Unified Model for Elementary Particles

The neutrino unified model for elementary particles is proposed and discussed with the connection of Sao Paulo and Nagoya Models. Since the model stands on the new interpretation of electric and baryonic charges, the consideration is concentrated to the roles of charges. Problems toward the unified theory along this model are also presented.