Tadashi Toyoda

Nonperturbative canonical formulation and Ward--Takahashi relations for quantum many-body systems at finite temperatures

Abstract A nonperturbative canonical field-theoretic approach to Matsubaras finite temperature quantum many-body theory is presented. The finite temperature Ward-Takahashi relations for the phase transformation, the Galilean transformation and general time-independent continuous transformations are derived for both fermions and bosons with interactions. The finite temperature Ward-Takahashi relations for nonconserved currents and the finite temperature Goldstones theorem are also discussed.

The plateau widths of the quantized hall conductance

Abstract A possible mechanism for the normal quantized Hall conductance is suggested from a viewpoint different from Laughlins theory, and a formula for the widths of the Hall conductance plateaus is presented, which shows good agreement with the recent experimental data by Stormer et al.

A microscopic theory of the quantized Hall effects

A microscopic theory of the normal quantized Hall effect based on the canonical equation of motion for the current operators is presented. The obtained formula gives the Hall resistance as a function of the gate voltage and shows good agreement with the MOSFET experiment by von Klitzing et al. The formula also gives the temperature dependence quantitatively and shows explicitly how the plateaus disappear at higher temperatures.

Retarded transverse current-current response functions of a two-dimensional electron gas

The retarded transverse current-current response functions of an ideal two-dimensional electron gas at zero temperature are calculated. Introducing a new approximation scheme which allows one to take account of the reaction of the electromagnetic field to the induced current, i.e. the influence of the electronic induced current on the dynamics of the electromagnetic field, within the framework of the conventional linear response theory in a self-consistent way, a possible form of the dispersion relation for the transverse plasmon in the system is obtained. It is found that the energy of the transverse plasmon has a gap at k=0, if the thickness of the system is finite, in contrast to the longitudinal case.

Remarks on Laughlin's wavefunction for anomalous quantized Hall effects

Abstract It is shown that Laughlins variational wavefunction for the anomalous quantized Hall effects is an exact ground state wavefunction of non-interacting two-dimensional electrons in a strong magnetic field.

The f-sum rule and Tao-Thouless theory for the anomalous quantized hall effects

Abstract It is shown that the Green function assumed by Tao and Thouless leads to a voilation of the current conservation in the Heisenberg picture.

The generalized dielectric function of the Tao-Thouless superlattice model for the anomalous quantized Hall effects

Abstract The generalized dielectric function is calculated within the framework of the microscopic theory of the fractional quantized Hall conductance proposed by Tao and Thouless. It is shown that the screening effect is minimal for the filling factor 1 2 , which suggests a possible mechanism for exclusion of the fractional quantum Hall conductance with the filling factor 1 2 .

The Ehrenfest theorem for the charged quantized Schrödinger field with arbitrary spin

The Ehrenfest theorem is extended to the many-body system of a charged Schrodinger field with arbitrary spin in the presence of self- and electromagnetic interactions. The second quantized formalism is used throughout to show that the statistics plays no role.

Transverse plasmon in two-dimensional electrons

Abstract We calculated the retarded transverse current-current response function of an ideal two-dimensional electron gas and obtained a dispersion relation for the transverse plasmon in the system.

Marginal Fermi-liquid model and Ward-Takahashi relations

Abstract It is shown that the vanishing of the quasi-particle weight at the Fermi surface is equivalent to the divergence of the vertex function using a finite-temperature Ward-Takahashi relation.