arXiv subjects

Kei-Ichi Kondo

Publications and source records attributed to Kei-Ichi Kondo.

133 records · Page 8Linked to original sources

arXiv1996

The Gauged Thirring Model

We propose the gauged Thirring model as a natural gauge-invariant generalization of the Thirring model, four-fermion interaction of current-current type. In the strong gauge-coupling limit, the gauged Thirring model reduces to the recently proposed reformulation of the Thirring model as a gauge theory. Especially, we pay attention to the effect coming from the kinetic term for the gauge boson field, which was originally the auxiliary field without the kinetic term. In 3 + 1 dimensions, we find the nontrivial phase structure for the gauged Thirring model, based on the Schwinger-Dyson equation for the fermion propagator as well as the gauge-invariant effective potential for the chiral order parameter. Within this approximation, we study the renormalization group flows (lines of constant physics) and find a signal for nontrivial continuum limit with nonvanishing renormalized coupling constant and large anomalous dimension for the gauged Thirring model in 3+1 dimensions, at least for small number of flavors $N_f$. Finally we discuss the (perturbatively) renormalizable extension of the gauged Thirring model.

hep-th↗

arXiv1995

Bosonization and Duality of Massive Thirring Model

Starting from a reformulation of the Thirring model as a gauge theory, we consider the bosonization of the $D$-dimensional multiflavor massive Thirring model $(D \ge 2)$ with four-fermion interaction of the current-current type. Our method leads to a novel interpolating Lagrangian written in terms of two gauge fields. Especially we pay attention to the case of very massive fermion $m \gg 1$ in (2+1) and (1+1) dimensions. Up to the next-to-leading order of $1/m$, we show that the (2+1)-dimensional massive Thirring model is mapped to the Maxwell-Chern-Simons theory and that the (1+1)-dimensional massive Thirring model is equivalent to the massive free scalar field theory. In the process of the bosonization of the Thirring model, we point out the importance of the gauge-invariant formulation. Finally we discuss a possibility of extending this method to the non-Abelian case.

hep-th↗

arXiv1995

First and Second Order Phase Transitions in Maxwell--Chern-Simons Theory Coupled to Fermions

In the Maxwell--Chern-Simons theory coupled to $N_f$ flavors of 4-component fermions (or even number of 2-component fermions) we construct the gauge-covariant effective potential written in terms of two order parameters which are able to probe the breakdown of chiral symmetry and parity. In the absence of the bare Chern-Simons term, we show that the chiral symmetry is spontaneously broken for fermion flavors $N_f$ below a certain finite critical number $N_f^c$, while the parity is not broken spontaneously. This chiral phase transition is of the second order. In the presence of the bare Chern-Simons term, on the other hand, the chiral phase transition associated with the spontaneous breaking of chiral symmetry is shown to continue to exist, although the parity is explicitly broken. However it is shown that the existence of the bare Chern-Simons term changes the order of the chiral transition into the first order, no matter how small the bare Chern-Simons coefficient may be. This gauge-invariant result is consistent with that recently obtained by the Schwinger-Dyson equation in the non-local gauge.

hep-ph↗

arXiv1995

Thirring Model as a Gauge Theory

We give another reformulation of the Thirring model (with four-fermion interaction of the current-current type) as a gauge theory and identify it with a gauge-fixed version of the corresponding gauge theory according to the Batalin-Fradkin formalism. Based on this formalism, we study the chiral symmetry breaking of the $D$-dimensional Thirring model ($2<D<4$) with $N$ flavors of 4-component fermions. By constructing the gauge covariant effective potential for the chiral order parameter, up to the leading order of $1/N$ expansion, we show the existence of the second order chiral phase transition and obtain explicitly the critical number of flavors $N_c$ (resp. critical four-fermion coupling $G_c$) as a function of the four-fermion coupling $G$ (resp. $N$), below (resp. above) which the chiral symmetry is spontaneously broken.

hep-th↗

arXiv1995

First-order Phase Transition in Three-dimensional QED with Chern--Simons Term

We have studied the chiral phase transition in three-dimensional QED in the presence of a Chern--Simons term for the gauge field. There exists a phase where the chiral symmetry is broken dynamically and we have determined the critical line for this symmetry breaking as a function of the effective coupling and the strength of the additional Chern--Simons term. In the presence of a Chern--Simons term, the chiral phase transition turns out to be first order, in sharp contrast to the phase transition in pure three-dimensional QED.

hep-ph↗

arXiv1995

Dynamical Breakdown of Chirality and Parity in (2+1)-dimensional QED

In the (2+1)-dimensional QED with and without the Chern-Simons term, we find the non-local gauge in which there is no wavefunction renormalization for the fermion in the framework of the Schwinger-Dyson equation. By solving the Schwinger-Dyson equation in the non-local gauge, we find a finite critical value $N_f^c$ for the number of flavors $N_f$ of four-component Dirac fermions, above which the chiral symmetry restores irrespective of presence or absence of the Chern-Simons term. In the same framework, we study the possibility of dynamical breakdown of the parity. It is shown that the parity is not dynamically broken. We discuss this reason from the viewpoint of the Schwinger-Dyson equation.

hep-ph↗

arXiv1994

Flavor-Dependence and Higher Orders of Gauge-Independent Solutions in Strong Coupling Gauge Theory

The fermion flavor $N_f$ dependence of non-perturbative solutions in the strong coupling phase of the gauge theory is reexamined based on the interrelation between the inversion method and the Schwinger-Dyson equation approach. Especially we point out that the apparent discrepancy on the value of the critical coupling in QED will be resolved by taking into account the higher order corrections which inevitably lead to the flavor-dependence. In the quenched QED, we conclude that the gauge-independent critical point $α_c=2π/3$ obtained by the inversion method to the lowest order will be reduced to the result $α_c=π/3$ of the Schwinger-Dyson equation in the infinite order limit, but its convergence is quite slow. This is shown by adding the chiral-invariant four-fermion interaction.

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