Ko Aizu

Canonical transformation invariance and linear multistep formula for integration of hamiltonian systems

Abstract It is shown that, if a linear multistep formula applied to numerical integration of hamiltonian systems is also to be a canonical transformation, it must essentially be a two-term formula.

Observations of flat-spectrum QSOs at 43 GHz at NRO

Abstract Using the 45-m telescope at NRO we measured flux densities at 43 GHz of 115 flat-spectrum radio sources selected from 5 GHz catalogues. A preliminary log N ∼ log S curve is obtained. A simple model interpretation of the curve is given.

The 10 GHz Log N — Log S Curve Obtained At NRO

Using 45-m radio-telescope at NRO, we obtained log N — log S curves at 10 GHz for flat- and steep-spectrum sources separately. A simple model-fitting of evolution is given

LOG N - LOG S OF RADIO SOURCES AT 10 GHz WITH FLAT SPECTRA*

A log N — log S relation at 10 GHz is constructed for sources with the flat spectra α ≤ 0.5 (flux density S ∞ ν −α) from observations at NRO, MPIfR and others. Based on the source distribution on log (Luminosity) ~ volume plane we obtain an epoch-depending luminosity function, which explains the above relation.

Nature of Central Radio Component of Double Extragalactic Radio Sources

The nature of the central component of double extragalactic radio sources (radio galaxies and QSO) is studied. Comparison of the radio luminosity of central components with that of compact QSO and that of the central components of E galaxies suggests that (a) in a broad scheme of radio evolution from QSO to elliptical galaxies through radio galaxies, we can consider the evolution of central components separately from that of extended components, and (b) the central components of double sources represent the middle phase between compact QSO and central components of E galaxies. A correlation between the radio luminosity of the central components and that of extended components is found.

RADIO EVOLUTION OF PULSARS.

Phenomenological analysis of radio evolution of pulsars is made. Under an assumption that the period of most of pulsars have a similar time dependence, the age t of pulsars is determined statistically from the observed spindown time t1 : t=0.30t1• Period P, radio luminosity during the pulse L, called simply the luminosity, and size of the radio-emitting region a, estimated as the pulse width times the light velocity, are shown to have time dependences of PoctO.SO±o.os, Loct0.70±0,t2 and aoct0.23±0.o& respectively. This radio evolution is compared with that of supernova remnants, quasi-stellar objects and radio galaxies directly or by means of the luminosity versus volume emissivity diagram. The evolutionary tracks are similar to each other in spite of different mechanisms involved. Finally the observed luminosity function N(L) ocL-t.50±0.os is compared with that calculated from the time dependence of the luminosity and it is shown that the slopes of the both functions are consistent with each other if the selection effect in the present sample of pulsars is taken into account. Similarly the birth rate of pulsars in the Galaxy is shown to be nearly equal to the explosion rate of type II supernovae after the selection effect is taken into account.

Field Operators for Bosons with Impenetrable Cores. II. Equations of Motion and General Operator Formalism

Continuing the investigation started in part I, we derive the equations of motion in the Fock representation and a nonrelativistic field theory for bosons interacting as hard spheres.

On a Possible Small Pauli Term in Quantum Electrodynamics

The substitution of a nonlocal interaction and a cutoff procedure for the local electron--photon interaction in the calculation of the electron mass in the low-energy limit introduces a small Pauli term, delta . The delta is calculated, first by using the precise anomalous magnetic moment of the electron, giving delta = 7.4 plus or minus 5 x 10⁻⁶, and then by using the Lamb sbift in the H atom, giving delta = --1 7 plus or minus 3 4 x 10⁻⁶ Calculation using the fine structure of positronium was also performed, resulting in delta = 2.5 plus or minus 9.8 x 10⁻⁵. It is concluded that there is no definite evidence for or against the existence of a Pauli term. The possible role of the Pauli term in quantum electrodynamical processes is discussed; it is similar to the modification in quantum electrodynamics at small distances. (D.L.C.)

Maximal Weak Interactions

>All possible weak processes are systematically enumerated, and the hypothesis of maximal set of interactions (that there is always the weak interaction among any combination of all kinds of particles) is investigated. It is found that this maximal interaction model is equivalent to the minimal interaction model in the sense that the experimental facts are described equally well by these two mcdels, provided that a selection rule which forbids at least the appearance of mu -e pair is added to the former model. (auth)

General theory of particle mixtures

SummaryThe general theory of particle mixtures is developed and their remarkable time behavior at decay is shown to be a natural consequence of degeneracy of the initial state. Applications to several simple cases, positronium in a magnetic field, K0 and K0 particle mixture and a possible θ-Τ doublet are discussed. In particular it is shown that, if the K0 has two lifetimes, the mass difference between K0 and K0 caused by a possible non-invariance of strong interaction under charge-conjugation can not exceed much the value 10-5 eV.RiassuntoSi sviluppa la teoria generale delle misoele di particelle e si dimostra che il loro notevole comportamento rispetto al tempo nel decadimento è una conseguenza naturale della degenerazione dello stato iniziale. Si discutono applicazioni a vari casi semplici: positronio in un campo magnetico, miscela di particelle K0 e K0 e un possibile doppietto θ-Τ. Si dimostra in particolare che se il K0 ha due vite medie la differenza di massa tra K0 e K0 dovuta a una possibile non-invarianza dell’interazione forte nella coniugazione della earioa non puÒ eccedere di molto il valore 10-5 eV.