Toyoki Matsuyama

Magnetic field induced multi-component QED3 and quantum Hall effect

Dynamics of two dimensional electrons under the strong perpendicular magnetic field is shown to be described by a multi-component fermion theory. The electric conductance has a remarkable property known as the quantum Hall effect. The Hall conductance is quantized in units ofe2/h in the gap region and in the localized state region. The proof of exactness is presented in general cases using quantum field theory.

A Microscopic Theory of the Quantum Hall Effect

Abstract A general proof of the integer quantization of the static Hall conductivity based on the Ward-Takahashi identity is given. The Ward-Takahasi identity is so general that electron-impurity and electron-electron interactions can be incorporated. Finite temperature and finite size effects are also studied and the experimental characteristics are shown to be reproduced. The value on the plateau agrees with an integer multiple of e 2 /2π h .

Rotating Black Hole in Extended Chern-Simons Modified Gravity

We investigate a slowly rotating black hole in four-dimensional extended Chern-Simons modified gravity. We obtain an approximate solution that reduces to the Kerr solution when a coupling constant vanishes. The Chern-Simons correction effectively reduces the frame-dragging effect around a black hole in comparison with that of the Kerr solution. Subject Index: 420, 453

Canonical structures and bose-Fermi transmutations in (2+1)-dimensional U(1) gauge theories

Abstract We investigate the canonical structures of U(1) gauge theories with the Chern-Simons term as the kinetic term of the gauge field, following the generalized hamiltonian formalism. In quantized theories, the gauge field which is expressed by using the charge density operator of matter in solving the Gauss law constraint, can be eliminated by a change of the matter variables. Then the condition of charge conservation which is guaranteed by gauge invariance leads us to the Bose-Fermi transmutation, which is found by investigating the equal-time (anti-) commutators. The specific feature of the theories is prominent by comparison with the usual case with the quadratic derivative term as the action of the gauge field.

Flat rotation curves in Chern-Simons modified gravity

Introduction.—There are three fundamental unsolved issues in the theory of gravity: quantization of gravity, dark energy, and dark matter. The string theory [1] is a promising candidate for a consistent quantum theory of gravity. Many attempts in quantizing gravity, however, have not been successful. In astronomy/astrophysics, a number of observations suggest the existence of dark energy [2, 3] and dark matter [3, 4]. Although many surveys of astrophysical objects have been conducted [5], it has not yet been revealed what is dark matter. For instance, the flat rotation curves of galaxies [6] have been considered to be a robust evidence of dark matter. The velocity v of a star orbiting around the center of a galaxy becomes a constant at a certain distance r far from the center. While the Newtonian gravity yields a relation v ∝ 1/ √ r. At present, we usually attribute the discrepancy to dark matter. However it may be still possible to explain the phenomenon based on a theory without dark matter. In this paper, we propose a model to solve this discrepancy in the framework of the Chern-Simons (CS) gravity.

Does a black hole rotate in Chern-Simons modified gravity?

The latest observational results of the cosmic microwave background (CMB) anisotropy from the Wilkinson Microwave Anisotropy Probe (WMAP) (1) are success- fully explained by thecold dark matter standard model. However, two big issues still remain: what is dark matter, and what is dark energy? According to the WMAP results, unfortunately about 96% of the contents of the Universe is given by the dark components that we still do not know. Therefore, properties of dark matter and dark energy have eagerly been investigated from observations (2,3). In contrast with the ordinary approaches (2,3), in which the existence of the dark components is assumed, it is of great interest to investigate alternative gravity theories (4 - 8) to solve the dark matter and dark energy problem. In this paper, we focus our attention on the Chern-Simons modi- fied gravity theory (9). This gravity theory was constructed by Deser et al. (9 )i n (2 � 1) spacetime dimensions for the first time by analogy with the topologically massive U(1) and SU(2) gauge theories. The Chern-Simons modified gravity theory was relatively recently extended by Jackiw and Pi (10 )t o (3 � 1) spacetime dimensions. In the ex- tended theory, the Schwarzschild solution holds without any modification (10). Therefore, the theory passes the classical tests of general relativity (11). In this gravity theory, however, the Kerr solution does not hold. Thus, the solution for a rotating black hole should have a differ- ent form from the Kerr solution. In � 2 � 1� -dimensional Chern-Simons modified gravity, a family of rotating black hole solutions was found by Moussa et al. (12). The solutions have a fascinating feature that observers in this spacetime behave like ones inside the ergosphere of the Kerr spacetime. This feature is similar to that of the rota- tion of galaxies (13). Therefore, it is very interesting to investigate rotating black hole solutions in the � 3 � 1� -dimensional Chern-Simons modified gravity theory. In this paper, we discuss rotating black hole solutions taking account of perturbation around the Schwarzschild solution. This paper is organized as follows. In Sec. II, we briefly review the � 3 � 1� -dimensional Chern-Simons modified gravity theory. In Sec. III, we consider the perturbation around the Schwarzschild solution to discuss slow rotation of the black hole. First we investigate a constraint equation independently of a choice of the embedding coordinate. In Sec. III A, from the first-order equations of the field equa- tion, we obtain the metric solution taking the embedding coordinate to be timelike. In Sec. III B, we investigate the metric solution for the case in which the embedding coor- dinate is spacelike. Finally, we provide a summary in Sec. IV. In this paper, we use a unit in which cG � 1.

Dynamical parity violation in QED3 with a two-component massless fermion☆

Abstract In QED 3 with a single two-component massless fermion, we investigate a dynamical effect on the parity symmetry using the truncated Schwinger-Dyson equation. In a lowest ladder approximation and the Landau gauge, there is no divergence and we find a non-trivial solution by a numerical method. Thus the parity symmetry is broken dynamically.

CHERN-SIMONS QUANTUM MECHANICS

The author considers the quantum mechanics coupled to the gauge field which has the Chern-Simons term as the action. The generalized Hamiltonian formalism of the system is constructed and canonical and path-integral quantizations are performed. In solving the Gauss law constraint, the gauge field is represented by a multivalued function and the charge density operator of the particle. The gauge potential is singular and also induces a singular magnetic field through the magnetic flux is finite. By a phase transformation, the singular gauge field is eliminated. Then the transformed wavefunction absorbing the gauge field induces a novel phase factor under 2 pi -rotation in space. Thus the author shows that the transformed wavefunction describes exotic spin state. The extension of these analyses to the relativistic case is also presented.

U(1) gauge-coupled Dirac equation and massless (QED)2 on a finite element

Abstract Toward the construction of the gauge theory on a lattice without species doubling, we formulate the U(1) gauge-coupled Dirac equation on a finite element in (d + 1)-dimensional space-time. For massless (QED)2, we derive the vector current conservation and the axial anomaly. The reproduction of the axial anomaly indicates the resolution of the doubling problem.

Mode-switching in the flow of water into a cup

Abstract Mode-switching was investigated when water was poured into a cup. Three modes, i.e., accumulation flow (Mode I), scattering flow (Mode II), and oscillatory flow (Mode III), were regulated by the flow rate. The bifurcation flow rate at Mode I → II was different from that at Mode II → I , i.e., hysteresis in mode-switching was observed. Mode III was observed at Mode I → II. The bifurcation point changed depending on the radius of the water tube, and the water-hollow was an important factor in mode-switching. The mode-switching was reproduced by a numerical calculation including the double-minimum profile of the free energy and the flow rate.