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Showing papers in "Progress of Theoretical Physics in 1967"


Journal ArticleDOI
TL;DR: In this article, a prescription is given to convert a non-invariant canonical (pseudo) energy-momentum tensor into an invariant one, and the symmetric part of these field equations is examined for the two cases: (1) under linear and non-relativistic approximation, it reduces to the classical gravitational field equation, (2) for static and spherically symmetric field, its solution is shown to correspond to Schwarzschild's solution.
Abstract: Gauge fields together with non-linear field equations to govern them are introduced by requiring that the Lagrangian should be invariant under ·an extended translation in spacetime, i.e. a translation in which four parameters are replaced by four arbitrary coordinatedependent functions. A prescription is given to convert a non-invariant canonical ("pseudo") energy-momentum tensor into an invariant one. The symmetric part of these field equations is examined for the two cases: (1) under linear and non-relativistic approximation, it reduces to the classical gravitational-field equation, (2) for static and spherically symmetric field, its solution is shown to correspond to Schwarzschild's solution. The antisymmetric part has no classical analogues, for there are no sources of skew-symmetric energy-momentum tensors in the classical experiments. A reasonable method is proposed to eliminate this redundant field.

225 citations



Journal ArticleDOI
TL;DR: In this article, it was shown that all non-relativistic central potential problems have both 0 4 and SU3 symmetries, and the internal invariances of these problems derive from a dynamical origin.
Abstract: It is found that all classical dynamic problems (relativistic as well as non-relativistic) in­ volving central potentials, inherently possess both 0 4 and SU3 symmetry. This leads to a generalization of both the Runge-Lenz vector in the Kepler problem and the conserved sym­ metric tensor in the harmonic oscillator problem. For a general central potential, an explicit construction of the elements of the Lie algebra of 0 4 and SUa in terms of canonical variables is given. The, question of a possible quantum-mechanical analog is discussed. Also, a con­ structive technique is given for imbedding the Lorentz group and SU3 in an infinite-dimensional Lie algebra. After the initial success of SU3 in particle physics, various attempts were made to embed both the internal and external symmetry groups within a larger structure in order to relate different SUa multiplets. How the internal and external symmetry groups interlock, and whether useful results can be obtained from a finite larger algebra has been the subject of much discussion.ll In related investigations, the whole question of internal invariance has come under close scrutiny. The internal invariances that are most clearly understood are those which arise in classical problems ; for these, the invariances derive from a dynamical origin. Recently, a number of classical problems have been extensively re-investigated from the group-structure point of view. Our paper will also be primarily concerned with internal invariances of classical dynamical problems. We shall show that all such central potential problems-relativistic as well as non-relativistic-inherently have both 0 4 and SU3 symmetries. An internal symmetry associated with the non-relativistic Kepler problem (which is responsible for its accidental degeneracy) has been known for a long

114 citations





Journal ArticleDOI
TL;DR: In this article, the evolution of the second-order density waves most naturally associated with the first-order rotational and gravitational waves, and the behavior of an isolated eddy is examined for a comparison with those of periodically distributed eddies.
Abstract: First it is indicated that, at the radiation-dominated stage of the expanding universe, two ways should be distinguished for the evolution of the second-order density waves most naturally associated with the first-order rotational and gravitational waves, and the behavior of an isolated eddy is examined for a comparison with those of periodically distributed eddies. Next the second-order waves associated with rotational, density and their mixed waves at the intermediate stage (before and after the decoupling epoch tD) are analyzed and the rapidity of compression due to the inertial force appearing soon after tD is calculated. Finally the possibility of galaxy formation is examined on the basis of the above analysis. Moreover a possibility for comparatively small galaxies to be formed through the cascade due to non-linear process is considered.

66 citations



Journal ArticleDOI
Ryuzo Abe1
TL;DR: In this paper, the singularity of specific heat near the transition point is studied in the case of the Ising model with ferromagnetic nearest neighbor interaction and the parameter appearing in high temperature expansion is extended to the whole complex plane and the analytical behavior of thermodynamic functions is examined.
Abstract: Logarithmic singularity of specific heat near the transition point is studied in the case of the Ising model with ferromagnetic nearest neighbor interaction. The parameter appearing in high temperature expansion is extended to the whole complex plane and the analytical behavior of thermodynamic functions is examined. A distribution of roots which are derived from a certain algebraic equation plays an important role of determining the singularity of specific heat. A strikingly simple distribution of roots is shown to lead to the singularity consistent with experiment. Comparison of the theory with experiment on the liquid-gas transition at the critical point is discussed.

63 citations


Journal ArticleDOI
Ryuzo Abe1
TL;DR: In this paper, the singularity of specific heat near the transition point is studied for the Ising or Heisenberg model with an arbitrary value of spin and range of interaction, and the following results are obtained for a reasonable distribution of zeros of canonical partition function.
Abstract: On the basis of Fisher's method, singularity of specific heat near the transition point is studied for the Ising or Heisenberg model with an arbitrary value of spin and range of interaction. The following results are obtained for a reasonable distribution of zeros of canonical partition function. (a) If the specific heat has a singularity C,_ (T -- Tc) -a above the transition point Tc, it should have a singularity C_ (Tc- T) -a below Tc, C_ being not necessarily equal to C+. (b) If the specific heat has a logarithmic singularity -A ln(T-Tc) +B+ above Tc, it should have a singularity -A ln(Tc- T) + B_ below Tc, B_ being not necessarily equal to B +· Some theoretical and experimental works so far reported are discussed in the light of these results.

51 citations




Journal ArticleDOI
TL;DR: In this paper, the parity-violating and parity-conserving amplitudes of non-leptonic hyperon and tr decays are discussed in the nonrelativistic quark model and the SU(6) theory, where the pole diagram for quark is considered.
Abstract: Nonleptonic hyperon and tr decays are discussed in the nonrelativistic quark model and the SU(6) theory, where we consider the pole diagram for quark. the four-body weak current­ current interaction J1 2 J3 1 and the meson exchange interaction_ We assume two models, and can explain the experiments for parity-violating and parity-conserving amplitudes of nonleptonic hyperon decays. In particular the L1I = 1/2 rule is derived, though the weak current-current interaction J1 2 J3 1 does not satisfy £11 = 1/2. As to the decay of tr two models predict the different ratio of r(SJ~A+K) and r(SJ~S+ll). One is consistent with experiment, the other forbids SJ~A+K.



Journal ArticleDOI
TL;DR: In this article, a theoretical approach to the problem of diffusion controlled bimolecular reactions is presented, where the probability of the first reaction is introduced as a fundamental quantity and an approximation which reduces the general formula to a problem of Markov process is adopted.
Abstract: A theoretical approach to the problem of diffusion controlled bimolecular reactions 1s presented. In order to take into account the ti:ne correlation of reaction process of our many-particle system, the probability of the fust reaction is introduced as a fundamental quantity. Time development of the ensemble of our system is formulated using the probability of the first reaction. An approximation which reduces the general formula to a problem of Markov process is adopted. Then it is shown that, if we assume stationary reaction rate, the usual phenomenological kinetic equation, i.e. the so called law of mass action can be derived as the first order approximation, and as the second order approximation the deviation from the law of mass action is examined. For the general case, in order to obtain the probability of the first reaction in an explicit form, it becomes necessary to solve. the multidimensional diffusion equation with pair absorbing interactions, which is calculated using the binary collision expansion method.

Journal ArticleDOI
Masuo Suzuki1
TL;DR: In this paper, the singularity of specific heat near the transition point is investigated in terms of the dis-tribution of zeros of the partition function in the complex temperature plane.
Abstract: Singularity of specific heat near the transition point is investigated in terms of the dis­ tribution of. zeros of the partition function in the complex temperature plane. In the case of a centrally symmetric two-dimensional distribution of zeros, the singularity of the radial dis­ tribution function of zeros reflects directly the anomaly of specific heat. Consequently, it is shown that in general the specific heat does not necessarily take the same critical indices above and below the transition point. The modified Slater KDP model solved exactly by Wu gives a nice example to our theory. The radial distribution function of zeros in the complex z(=eC!lcT) plane for this model is given by the equation g(r) =1/(rc2rv4-=i2). Then, the sin­ gularity of the specific heat for this model takes the form C+"'(T-Tc)- 1 1 2 for T>Tc and



Journal ArticleDOI
TL;DR: In this paper, a simple general expression for the effective exchange energy between a distant pair of moments which generally decays as R3 with the oscillations given by the stationary radii of the Fermi surface is derived.
Abstract: Interaction energy between two localized moments is calculated on the tight-binding or W olff-Clogston model by using the I-Iartree-Fock approximation. A simple general expression is obtained for the effective exchange energy between a distant pair of moments which generally decays as R3 with the oscillations given by the stationary radii of the Fermi surface. Interaction between an adjacent pair of moments is shown to be of local character and its sign is primarily governed by the electronic occupation in the impurity states. A general rule for the sign of the coupling between two moments proposed earlier on the basis of the Anderson model is strongly supported. Possible discontinuous occurrence of localized moments in some alloys is also discussed on the same model.

Journal ArticleDOI
Ryuzo Abe1
TL;DR: In this article, the critical behavior of pair correlation function in the presence of magnetic field, and compare their results with those of other theories with the same notations and definitions as in I, unless otherwise mentioned.
Abstract: 2) We will study in § 3 the critical behavior of pair correlation function in the presence of magnetic field, and compare our results with those of other theories. Throughout §§ 2 and 3 we will use the same notations and definitions as in I, unless otherwise mentioned. The second purpose of this paper is to discuss the pair correlation function from a diagrammatic point of view. Some time ago, the present author published a paper 3 ) (to be referred to as D) in which a diagrammatic method is developed for studying the phase transition of Ising model. We were led there to the Curie-Weiss law for the susceptibility, which is not consistent with the singularity (T-Tc)-\ Cr>1). We will remedy in § 4 this inconsistency and discuss a relevance of the results in § 3 with those obtained by a diagrammatic method.




Journal ArticleDOI
TL;DR: In this paper, the physical mechanism of drift wave instability was studied from the particle point of view by following the method used by Dawson in his theory of Landau damping, where the plasma particles were divided into two groups, resonant particles and non-resonant particles.
Abstract: : The physical mechanism of drift wave instability is studied from the particle point of view by following the method used by Dawson in his theory of Landau damping. The plasma particles are divided into two groups, resonant particles and non-resonant particles. Assuming that a drift wave starts initially while resonant particles are undisturbed, the trajectories of the particles are computed within the framework of linear theory. Such a drift wave of longitudinal mode is considered that propagates obliquely to a static magnetic field and in the plane normal to density gradient. (Author)


Journal ArticleDOI
Zensuke Tokuoka1
TL;DR: In this article, a new wave equation of a neutrino, which is a natural counterpart of the electromagnetic equation, is proposed, and the field is quantized only by generalizing the Hilbert space.
Abstract: A new wave equation of a neutrino, which is a natural counterpart of the electromagnetic equation, is proposed. Though the ordinary two-component neutrino equation is itself P- and C-invariant, the new equation is not invariant against parity and charge conjugation separately but is CP-invariant. The accepted V-A interaction is explained as a potential interaction of our neutrino. The field is quantized only by generalizing the Hilbert space.


Journal ArticleDOI
Hisao Okamoto1
TL;DR: In this article, a semi-phenomenological model was proposed to derive the attenuation constant of the longitudinal sound attenuation in ferroand antiferromagnets near the critical points.
Abstract: Recently Tani and Morill reported the temperature dependence of the longitudinal sound attenuation in ferroand antiferromagnets near the critical points taking into account the distortion of the exchange interaction in a microscopic manner (using the continued fraction method2l). We consider the same model but in a semi-phenomenological way, from which we derive a different result. Following Tani and Mori's idea1l we write down the expression for the attenuation constant