Statistics of the Composite Systems and Anyons in the Fractional Quantum Hall Effect

The commutation relations of the composite fields are studied in the 3, 2 and 1 space dimensions. It is shown that the field of an atom consisting of a nucleus and an electron fields satisfies, in the space-like asymptotic limit, the canonical commutation relations within the sub-Fock-space of the atom. The field-particle duality in the bound state is discussed from the statistics point of view. Then, the commutation relations of the scalar object in the Schwinger(Thirring) model are mentioned briefly and are shown consistent with its interpretation as the Nambu-Goldstone boson. The composite anyon fields are shown to satisfy the proper anyonic commutation relations with the additive phase exponents. Then, quasiparticle picture of the anyons is clarified under the restriction of this additibity. The difference between field and particle aspects becomes more prominent in the 2 space dimension. It is argued that the hierarchy of the fractional quantum Hall effect is rather simply understood by utilizing the quasiparticle charactors of the anyons when the background-boson gauge is assumed. In contrast to it, the coposite fermion theories are critically reviewedComment: 15 pages; The revised and enlarged version of hep-th/010516

Two-Body Dirac Equation and Its Wave Function at the Origin

A relativistic equation is deduced for the bound state of two particles, by assuming a proper boundary condition for the propagation of the negative-energy states. It reduces to the (one-body)Dirac equation in the infinite limit of one of the constituent mass. It also has the symmetries to assure the existence of the anti-bound-state with the same mass. The interaction kernel(pseudo-potential) is systematically constructed by diagonalizing the Hamiltonian of the background field theory, by which the retardation effects are included in the interaction. Its wave function at the origin(WFO) behaves properly in a manner suggested by the covariant field theory. The equation can well be applied in the heavy quark effective theory.Comment: LaTeX, 12 page

S-wave velocity structure estimated from long-period coda waves

Long-period coda waves were recorded on the vertical-component seismograms of aftershocks of the Hyogo-ken Nanbu earthquake, 1995. We identify the long-period coda waves as Rayleigh wave, because they appear after the S-arrival times and exhibit the normal dispersion that propagation velocity of the coda waves increases with an increase in period. By applying the moving window analysis to the coda waves from nine aftershocks, the group velocities are determined as a function of period within the range of 2 to 8 s. The group velocity dispersion data are inverted to investigate the S-wave velocity structure of the upper crust. The S-wave velocity structure is consistent with those obtained in previous studies using traval time analysis of bood waves

An Analysis of Trends in Research on Methods of Assessing Children’s Assertion

In recent years, there have been concerns about issues related to communication with others in education and childcare, especially the communication of younger children. One of the things that seem to be important in solving these problems is to raise the assertion of children. In order to nurture assertion, it is necessary to consider programs such as training. At the same time, it is important to assess the assertion of children. Therefore, in this study, the present state of the method for assessing the assertion of children was examined through analyzing the research trend. Since there were a few studies on young children subjects in this field, the study including the research of child subjects was examined.This research is a part of a research funded by JSPS Grant-in-Aid for Young Scientists (B) (17K13916). This is a revised version of a paper presented at the second research conference of The Japanese Society for the Study on Hoikusha Education in 2018