Chiral anomalies in the reduced model

On the basis of an observation due to Kiskis, Narayanan and Neuberger, we show that there is a remnant of chiral anomalies in the reduced model when a Dirac operator which obeys the Ginsparg-Wilson relation is employed for the fermion sector. We consider fermions belonging to the fundamental representation of the gauge group U(N) or SU(N). For vector-like theories, we determine a general form of the axial anomaly or the topological charge within a framework of a U(1) embedding. For chiral gauge theories with the gauge group U(N), a remnant of gauge anomaly emerges as an obstruction to a smooth fermion integration measure. The pure gauge action of gauge-field configurations which cause these non-trivial phenomena always diverges in the 't Hooft $N\to\infty$ limit when d>2.Comment: 20 pages, uses JHEP.cls and amsfonts.sty, the final version to appear in JHE

Canonical treatment of two dimensional gravity as an anomalous gauge theory

The extended phase space method of Batalin, Fradkin and Vilkovisky is applied to formulate two dimensional gravity in a general class of gauges. A BRST formulation of the light-cone gauge is presented to reveal the relationship between the BRST symmetry and the origin of $SL(2,R)$ current algebra. From the same principle we derive the conformal gauge action suggested by David, Distler and Kawai.Comment: 11 pages, KANAZAWA-92-1

Mechanism of resonant x-ray magnetic scattering in NiO

We study the resonant x-ray magnetic scattering (RXMS) around the K edge of Ni in the antiferromagnet NiO, by treating the 4p states of Ni as a band and the 3d states as localized states. We propose a mechanism that the 4p states are coupled to the magnetic order through the intra-atomic Coulomb interaction between the 4p and the 3d states and through the p-d mixing to the 3d states of neighboring Ni atoms. These couplings induce the orbital moment in the 4p band, and thereby give rise to the RXMS intensity at the K edge in the dipolar process. It is found that the spin-orbit interaction in the 4p band has negligibly small contribution to the RXMS intensity. The present model reproduces well the experimental spectra. We also discuss the azimuthal angle dependence of the intensity.Comment: 10 pages (revtex) and 7 postscript figure

X-Ray Magnetic Circular Dichroism at the K edge of Mn3GaC

We theoretically investigate the origin of the x-ray magnetic circular dichroism (XMCD) spectra at the K edges of Mn and Ga in the ferromagnetic phase of Mn3GaC on the basis of an ab initio calculation. Taking account of the spin-orbit interaction in the LDA scheme, we obtain the XMCD spectra in excellent agreement with the recent experiment. We have analyzed the origin of each structure, and thus elucidated the mechanism of inducing the orbital polarization in the p symmetric states. We also discuss a simple sum rule connecting the XMCD spectra with the orbital moment in the p symmetric states.Comment: 5 pages, 5 figures, accepted for publication in Physical Review

Spin Excitations and Sum Rules in the Heisenberg Antiferromagnet

Various bounds for the energy of collective excitations in the Heisenberg antiferromagnet are presented and discussed using the formalism of sum rules. We show that the Feynman approximation significantly overestimates (by about 30\% in the $S={1\over2}$ square lattice) the spin velocity due to the non negligible contribution of multi magnons to the energy weighted sum rule. We also discuss a different, Goldstone type bound depending explicitly on the order parameter (staggered magnetization). This bound is shown to be proportional to the dispersion of classical spin wave theory with a q-independent normalization factor. Rigorous bounds for the excitation energies in the anisotropic Heisenberg model are also presented.Comment: 26 pages, Plain TeX including 1 PostScript figure, UTF-307-10/9

4p states and X-Ray Spectroscopy

The 4p states in transition metals and their compounds usually play minor roles on their physical quantities. Recent development of resonant x-ray scattering (RXS) at the K-edge of transition metals, however, casts light on the 4p states, because the signals on orbital and magnetic superlattice spots are brought about by the modulation in the 4p states. The 4p states are extending in solids and thereby sensitive to electronic states at neighboring sites. This characteristic determines the mechanism of RXS that the intensity on the orbital superlattice spots are mainly generated by the lattice distortion and those on magnetic superlattice spots by the coupling of the 4p states with the orbital polarization in the 3d states at neighboring sites. Taking up typical examples for orbital and magnetic RXS, we demonstrate these mechanisms on the basis of the band structure calculation. Finally, we study the MCD spectra at the K-edge, demonstrating that the same mechanism as the magnetic RXS is working.Comment: 9 pages, 9 figures, submitted to Physica Scripta (comment

The Development of Kaji Kito in Nichiren Shu Buddhism

While the historical and religious roots of kaji kito (“ritual prayer”) lay in Indian and Chinese Esoteric Buddhist practices, the most direct influence of kaji kito in Nichiren Shu Buddhism, a Japanese Buddhist sect founded by the Buddhist monk, Nichiren (1222-1282), comes from Shingon and Tendai Buddhism, two traditions that precede Nichiren’s time. The historical development and initial incorporation of kaji kito into Nichiren Buddhism suggest that the main objective was to bring happiness to people through the use of prayer. Analysis of kaji kito following the death of Nichiren has shown that although different methods of kaji kito have developed, this notion of bringing happiness has been maintained. Changes made to the kaji kito of Nichiren Buddhism will be explained along with a discussion of the physical practice of kaji kito called aragyo, a 100-day ascetic practice undergone annually in Japan by some Nichiren Shu priests

Magnetic Impurity in the two-dimensional Heisenberg Antiferromagnet

We analyze the ground state properties of the two-dimensional quantum antiferromagnet with a S=1/2 Kondo impurity. Perturbation theory around the strong Kondo coupling limit is developed and the results compared with studies, based on exact diagonalization of small clusters. We find that at intermediate coupling the impurity is partially screened and the magnetization locally suppressed. A local singlet between the impurity and the host spin is formed asymptotically.Comment: 12 REVTex pages, 4 Postscript figure

Spin Waves in Quantum Antiferromagnets

Using a self-consistent mean-field theory for the $S=1/2$ Heisenberg antiferromagnet Kr\"uger and Schuck recently derived an analytic expression for the dispersion. It is exact in one dimension ($d=1$) and agrees well with numerical results in $d=2$. With an expansion in powers of the inverse coordination number $1/Z$ ($Z=2d$) we investigate if this expression can be {\em exact} for all $d$. The projection method of Mori-Zwanzig is used for the {\em dynamical} spin susceptibility. We find that the expression of Kr\"uger and Schuck deviates in order $1/Z^2$ from our rigorous result. Our method is generalised to arbitrary spin $S$ and to models with easy-axis anisotropy \D. It can be systematically improved to higher orders in $1/Z$. We clarify its relation to the $1/S$ expansion.Comment: 8 pages, uuencoded compressed PS-file, accepted as Euro. Phys. Lette