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Tatsuo Suzuki

Publications and source records attributed to Tatsuo Suzuki.

29 records · Page 2Linked to original sources
arXiv2004

A New Symmetric Expression of Weyl Ordering

For the creation operator $\adag $ and the annihilation operator $a$ of a harmonic oscillator, we consider Weyl ordering expression of $(\adag a)^n$ and obtain a new symmetric expression of Weyl ordering w.r.t. $\adag a \equiv N$ and $a\adag =N+1$ where $N$ is the number operator. Moreover, we interpret intertwining formulas of various orderings in view of the difference theory. Then we find that the noncommutative parameter corresponds to the increment of the difference operator w.r.t. variable $N$. Therefore, quantum (noncommutative) calculations of harmonic oscillators are done by classical (commutative) ones of the number operator by using the difference theory. As a by-product, nontrivial relations including the Stirling number of the first kind are also obtained.

quant-ph↗
arXiv2001

Integrable Submodels of Nonlinear $σ$-models and Their Generalization

In this thesis, we investigate various integral submodels and generalize them. In part I, we study the submodel of the nonlinear $\mathbf{C}P^1$-model and the related submodels in $(1+2)$ dimensions. In part II, we construct integrable submodels of the nonlinear Grassmann models in any dimension. We call them the Grassmann submodels. To show that our submodels are integrable, we construct an infinite number of conserved currents in two ways. One is that we make full use of the Noether currents of the nonlinear Grassmann models. The other is that we use a method of multiplier. Next we investigate symmetries of the Grassmann submodel. By using the symmetries, we can construct a wide class of exact solutions for our submodels. In part III, keeping some properties of our submodels, we generalize our submodels to higher-order equations. First we prepare the Bell polynomials and the generalized Bell polynomials which play the most important roles in our theory of generalized submodels. Next we generalize the $\mathbf{C}P^1$-submodel to higher-order equations. Lastly we generalize the Grassmann submodel to higher-order equations. By using the generalized Bell polynomials, we can show that the generalized Grassmann submodels are also integrable. As a result, we obtain a hierarchy of systems of integrable equations in any dimension which includes Grassmann submodels. These results lead to the conclusion that the integrable structures of our generalized submodels are closely related to some fundamental properties of the Bell polynomials.

hep-th↗
arXiv2000

A Generalization of the Submodel of Nonlinear CP^1 Models

We generalize the submodel of nonlinear CP^1 models. The generalized models include higher order derivatives. For the systems of higher order equations, we construct a Bäcklund-like transformation of solutions and an infinite number of conserved currents by using the Bell polynomials.

hep-th↗
arXiv1998

Submodels of Nonlinear Grassmann Sigma Models in Any Dimension and Conserved Currents, Exact Solutions

In the preceding paper(hep-th/9806084), we constructed submodels of nonlinear Grassmann sigma models in any dimension and, moreover, an infinite number of conserved currents and a wide class of exact solutions. In this paper, we first construct almost all conserved currents for the submodels and all ones for the one of ${\bf C}P^1$-model. We next review the Smirnov and Sobolev construction for the equations of ${\bf C}P^1$-submodel and extend the equations, the S-S construction and conserved currents to the higher order ones.

hep-th↗
arXiv1998

Nonlinear Grassmann Sigma Models in Any Dimension and An Infinite Number of Conserved Currents

We first consider nonlinear Grassmann sigma models in any dimension and next construct their submodels. For these models we construct an infinite number of nontrivial conserved currents. Our result is independent of time-space dimensions and, therfore, is a full generalization of that of authors (Alvarez, Ferreira and Guillen). Our result also suggests that our method may be applied to other nonlinear sigma models such as chiral models, $G/H$ sigma models in any dimension.

hep-th↗