Hiroomi Umezawa

Quantum statistics of fields and multiple production of mesons

SummaryThermodynamical relations in quantum field theory will be discussed. This gives a possibility to decide whether or not the interactions are renormalizable, i.e., of the first or the second kind. The renormalization procedure is elucidated by formulating the perturbational calculation. The possibility for proceeding to the non-perturbational method is also pointed out. These general considerations are applied to find out the interaction effects in the multiple production phenomena, which have been disregarded in Fermi-Landau’s statistical theory.RiassuntoSi discutono le relazioni termodinamiche nella teoria quantistica dei campi. È offerta così la possibilità di decidere se le interazioni siano rinormalizzabili o meno, cioè se siano di prima o di seconda specie. Si illustra il procedimento di rinormalizzazione formulando il calcolo perturbativo. Si mette anche in evidenza la possibilità di procedere con metodo non perturbativo. Queste considerazioni d’indole generale si applicano alla ricerca degli effetti d’interazione nei fenomeni di produzione multipla, effetti che furono trascurati nella teoria statistica di Fermi-Landau.

Commutation relations and relativistic wave equations

Abstract Covariant commutation relations for particles of any spin are given in the cases where the particles have only one mass state or have a mass spectrum.

A formulation for the bound-state problems

SummaryHere is proposed a theory for the system including the composite particles. Presuming that the outgoing operatorAout(x) of the elementary particle A is known as a series in powers of the operators att=0,A(x, 0) and Ȧ(x, 0), we show that the commutation relations among the outgoing operators of elementary and composite particles give us all the information about the composite particles.RiassuntoSi propone qui una teoria del sistema comprendente le particelle composte. Supponendo che l’operatore di uscitaAout(x) della particella elementare A sia noto come serie di potenze degli operatori pert=0,A(x, 0) e Ȧ(x, 0), si dimostra che le relazioni di commutazioni fra gli operatori di uscita delle particelle elementari e composte, ci danno tutte le informazioni sulle particelle composte.

An Approach to the Elementarity of Particles

As tools for judging whether a given particle is elementary or composite, a variety of equations, off-shell unitarity conditions, and bound- state equations are presented. The elementarity of deuteron is examined for the sake of testing the method proposed here, the result being satisfactory. (auth)

On the Hartree-Fock solution in field theory

Abstract It is pointed out that the inequivalent representation inherent in quantum field theory plays an essential role in the many-body problem. From this point of view is discussed the Bardeen model of superconductors and the Hartree solution is obtained as a rigorous one.

THE MASS LEVELS AND THE BROKEN SYMMETRY IN TERMS OF INEQUIVALENT REPRESENTATIONS

Abstract It is pointed out that inequivalent representations inherent in the theory of quantized fields in an infinite volume play an essential role in deriving mass levels and broken symmetries. A set of continuous parameters is introduced to specify these representations. By the requirement that the Hamiltonian shall tend to that of asymptotic fields as the volume becomes infinite, suitable representations are singled out. This requirement further determines possible values of the mass, which exhibit, in general, broken symmetries. It is also shown that with our method Nambus “Superconductor theory” of elementary particles can be formulated in a consistent manner.

Potential representation in quantum field theory

SummaryIn the realm of quantum field theory, we prove that the adiabatic theorem holds for vacuum and one-particle states. With the help of this theorem, we construct a representation in which interactions vanish as particles go away from each other. In this sense, the interactions in our representation can be compared to the potential energies in quantum mechanics of particles. Thus, our representation is called potential representation. The interaction operator here is found to be quite similar but not completely identical to Heitler’s reaction matrix. The use of our representation is illustrated by examining the scattering problems in Lee’s model.RiassuntoNel campo della teoria quantistica dei campi, dimostriamo che il teorema adiabatico è valido per il vuoto e gli stati ad una particella. Con l’aiuto di questo teorema costruiamo una rappresentazione in cui le interazioni si annullano quando le particelle si allontanano una dall’altra. In questo senso, nella nostra rappresentazione le interazioni possono essere paragonate alle energie potenziali nella meccanica quantistica delle particelle. Perciò la nostra rappresentazione si chiama rappresentazione del potenziale. Qui si trova che l’operatore di interazione è quasi simile ma non completamente identico alla matrice di reazione di Heitler. Si illustra l’uso della nostra rappresentazione esaminando i problemi di scattering nel modello di Lee.

On the Strong Interaction

A series of equations is proposed for the description of strong hyperon- meson interactions, in which the global symmetry theory is rejected. (D.L.C.)

General theory of the gauge transformation for vector meson fields

Abstract The general theory of gauge transformations for multiplet vector fields is considered by extending the three-dimensional rotation group of the Yang-Mills type into any simple Lie group. The neutral vector theory, the Yang-Mills theory of the triplet field and the Gell-Mann theory of the octad field are obtained as special cases of our general theory. Main results concerning the latter theory are stated in the form of equivalence theorems. The theory is not renormalizable when the masses of the vector fields are not zero. General features of the theory are briefly reviewed in the last section.

ON THE "NEUTRINO CHARGE" IN WEAK AND STRONG INTERACTIONS

Abstract It is proposed here to extend the idea of the neutrino charge of the leptons to all the elementary particles. No experiments have been found to contradict the assumption that parity is conserved when the neutrino charge is and that the neutrino charge changes by a constant in any process due to the weak interactions in which the conservation of the parity is violated. It is likely that the neutrino charges of the baryons and mesons can be assigned to be the same as their hypercharges.