Jiro Sakamoto

Bosonic Structure of a 2-Dimensional Fermion Model with Interaction among Different Species

We study a massive Thirring-like model in 2-dimensional space-time, which contains fermions with arbitrary number (N) of different species. This model is an extension of that of a previous paper, where we have considered two-species case. By this extension we expect that we can expose more general structures of this kind of model. We obtain the equivalent boson model with N species to our fermion model. We find that the coupling constant must be set in some regions in order for the model to be physically sensible. It seems hard to find such regions from direct obsavation of the original fermion model. We also find that for specific values of the coupling constant some of the boson fields disappear from the system. Therefore, the N-species fermion model is described by the boson model with fewer species.

A New Bosonization Procedure of Two-Dimensional Fermion Models in the Path Integral Formulation.

We present a new bosonization procedure for two-dimensional fermion models in the path integral formulation. We introduce external sources for the fermion currents instead of the auxiliary boson fields used in the conventional procedure. The calculations become much simpler because the external sources do not interact with themselves, while the auxiliary boson fields do, and we can find the equivalent boson models directy. All the formulations are done in Minkowski space-time. The extended Bukhvostov-Lipatov model and the massive Thirring model are discussed here as typical two-dimensional fermion models with currentcurrent-type interactions. The Rothe and Stamatescu model is also discussed, though this is slightly out of the context of bosonization, and the relation of the fermion current in the Heisenberg picture with that in the interaction picture is derived almost straightforwardly. Usually in the operator formalism, this relation is derived using the splitting procedure, which requires detailed calculations. It is expected that we can derive the boson model equivalent to the fermion model with SU(N) symmetry more easily and without any guess work.

Stochastic aspects of spatial fluctuations in the inflationary universe

Abstract We discuss the spatial fluctuation of a scalar field in the de Sitter background from the stochastic point of view. The two point Green function obtained by the quantum field theoretic approach is reproduced but is supplemented by the initial condition. The latter is smeared out if we consider a direct interaction induced by the self-coupling λφ 4 . This interaction imposes a new constraint.

Relativistic Bound State Solutions of a Two-Dimensional Fermion Model with Color SU(3) Symmetry

We implement color SU(3) symmetry on a relativistic two-dimensional fermion model proposed by Glockle, Nogami and Fukui (GNF). We find that it is possible to construct solutions for several multiplets of two and three particles by using the solutions for the GNF model. Though our model is based on the single-particle theory (i.e., the model does not contain any anti-particles), we regard a particle belonging to 3 as an anti-particle while the particles belong to 3 representation of the SU(3) group. There are conditions for the coupling constant that must be satisfied in order that a solution is acceptable as a physical bound state. We construct bound state solutions of 3 for a particle-particle pair, 1 for a particle-anti-particle pair and 1 for a three-particle system. We find that the singlet states form the tightest bound states among these solutions. We believe that our result provides some useful information for understanding quark confinement.

Generally covariant formulation in stochastic quantization of gravity

On reforme la quantification stochastique de la gravitation dans un espace-temps pseudo-Riemann en utilisant la modification de Huffet et Rumpf. La formulation est faite sous une forme covariante en considerant gμν et gμν comme des variables independantes