- 著者
- Hushimi Kodi Syozi Itiro Department of Physics Osaka University Department of Physics Osaka University
- 出版者
- Publication Office, Progress of Theoretical Physics
- 雑誌
- 理論物理学の進歩 (ISSN:0033068X)
- 巻号頁・発行日
- vol.5, no.2, pp.177-186, 1950-04
- 被引用文献数
- 3 33
After the matrix method in crystal statistics was introduced by R. Kubo^(1) Kramers and Wannier^(2), and others, Onsager^(3), using the abstract algebraic method, got the exact solution in the case of plane square net. His rather complicated method was simplified by Nambu^(6) considerably. We, independenty, attained the simplification of Onsager's method and have applied to the honeycomb lattice. And the exact solution has been obtained. From this, by the so called dual transformation we can get the partition function for triangular net. The Curie point occurs at ch 2H=2 in the honeycomb lattice and at exp (4H)=3 in the triangular net. These coincide with the resnlts obtained by the dual and star-triangle transformations^(4). The specific heat becomes logarithmically infinite but the energy itself remains continuous at this temperature. In the antiferromagnetic case, the honeycomb lattice behaves similar to the former case but the triangular net exhibits no phase change.
- 著者
- Takabayasi Takehiko
- 出版者
- 一般社団法人日本物理学会
- 雑誌
- 理論物理学の進歩 (ISSN:0033068X)
- 巻号頁・発行日
- vol.49, no.5, pp.1724-1745, 1973-05-25
- 被引用文献数
- 1
Classical theory of a relativistic string is formulated based on the parameter representation x_μ=x_μ(σ,τ) for the world strip swept by its motion. The necessity of the physically unam-biguous interpretation of this many-time formalism requires certain conditions. Invariance under the scale transformation of parameters is stressed. The physical meaning of τ is clarified. Besides the equation of motion and boundary condition which follow from the variational principle additional constrain t equations are needed to ensure a well-defined model without tachyonic solutions. The quantization of this classical theory is made in the usual way in the Heisenberg picture with respect to τ. Then by going over to the Schrodinger picture the parameter τ is automatically eliminated and we are left with a wave equation alone. Moreover this equation and the constraint equation are incorporated into a single "detailed wave equation", which was given previously as the fundamental equation of the quantum mechanics of a relativistic string. Case of external interaction is briefly treated.
- 著者
- Takabayashi Takehiko
- 出版者
- 一般社団法人日本物理学会
- 雑誌
- 理論物理学の進歩 (ISSN:0033068X)
- 巻号頁・発行日
- vol.51, no.1, pp.262-283, 1974-01
- 被引用文献数
- 4
In this and succeeding papers we reconstruct the theory of relativistic string, taken as a model of hadrons, in a general and unifying framework. In this paper the classical foundation of the "realistic" string theory is clarified. The theory is derived from the action integral which is invariant under "partial general transformation" on the parameters (σ,τ) for the world sheet traced by a motion of the string, and the fundamental equations are originally covariant under this group. Then by choosing a suitable gauge we obtain Lorentz-covariant formalism associated with constraints. We analyze its characteristics and obtain solutions. Taking another gauge we get the equivalent "Lorentz non-cavariant formalism" free from constraint. This directly exhibits the physical meaning of the theory and also leads to its standard Hamiltonian formalism. Several conservation laws characteristic to our string theory are given.
- 著者
- Takabayasi Takehiko
- 出版者
- 一般社団法人日本物理学会
- 雑誌
- 理論物理学の進歩 (ISSN:0033068X)
- 巻号頁・発行日
- vol.47, no.3, pp.1026-1046, 1972-03-25
- 被引用文献数
- 2
The theory of detailed wave equation (DWE), which represents relativistic quantum dynamics of an extended system with external interaction for a specific value of Regge intercept, avoiding ghost states and leading to dual amplitude, is further developed in several respects. The original formulation (the σ-formalism) for the string model is transcribed into a few equivalent formalisms. In the λ-formalism the invariance of DWE against the "Hilbert transform" becomes manifest. Finite "gauge transformations", under which the theory is invariant, are explicitly obtained for the consideration of their structural meaning. The original string model is generalized to the hybrid model, where each element constituting the string is endowed with internal "Fermi oscillator variables", in the framework of DWE, which now fixes the Regge intercept at the value lower than the original one by 1/2 unit or its multiples. In particular the hybrid model with vector Fermi variables, which implies "double-string" consisting of Dirac-like elements, is treated, where our vector Fermi variables differ from those in similar models by other authors with respect to their reality and Lorentz properties and are free from the introduction of additional indefinite metric. Moreover our theory is invariant under space reflection.
- 著者
- Tomonaga Sinitiro
- 出版者
- 一般社団法人日本物理学会
- 雑誌
- 理論物理学の進歩 (ISSN:0033068X)
- 巻号頁・発行日
- vol.5, no.4, pp.544-569, 1950-08
- 被引用文献数
- 16 278
The fact implied by Bloch several years ago that in some approximate sense the behavior of an assembly of Fermi particles can be described by a quantized field of sound waves in the Fermi gas, where the sound field obeys Bose statistics, is proved in the one-dimensional case. This fact provides us with a new possibility of treating an assembly of Fermi particles in terms of the equivalent assembly of Bose particles, namely, the assembly of sound quanta. The field equation for the sound wave is found to be linear irrespective of the absence or presence of mutual interaction between particles, so that this method is a very useful means of dealing with many-Fermion problems. It is also applicable to the case where the interparticle force is not weak. In the case of force of too short a range this method fails.
- 著者
- Horiuchi Hisashi SUZUKI Yasuyuki
- 出版者
- 一般社団法人日本物理学会
- 雑誌
- 理論物理学の進歩 (ISSN:0033068X)
- 巻号頁・発行日
- vol.49, no.6, pp.1974-2004, 1973-06-25
- 被引用文献数
- 33
Alpha-decay widths of SU_3, deformed oscillator and cluster model wave functions are calculated quantitatively for the ground band levels of ^<8>Be and the first K=0^<-> band levels of ^<20>ne. Tails of the reduced width amplitudes of these model wave functions are amended by two methods, of which one is to connect smoothly the inner original reduced width amplitude with the resonance tail given by the release energy of α particle, and the other is to apply the Green's-function method developed by Kawai and Yazaki for the calculation of the radial form factor for the stripping or pick up reactions. From comparisons of the calculated results with experiments it is concluded that the SU_3 model is insufficient to reproduce large α-decay widths. It is further shown that the deformed oscillator model is also considered to be inappropriate for the general explanation of the (rotational) levels with large cluster widths. From these consequences on SU_3 and deformed oscillator models and by the numerical confirmation that the cluster model wave functions can naturally reproduce the experiments consistently with the variational energy calculations, the importance of the molecular viewpoint in light nuclei is emphasized.