arXiv subjects

Kazuyasu Shigemoto

Publications and source records attributed to Kazuyasu Shigemoto.

30 records · Page 2Linked to original sources

arXiv2019

Integrability Condition in the Statistical Model and the Addition Formula of g = 2 Hyperelliptic Function

The integrability condition of the Ising model is understood as the SU(2) integrability condition and also as the model parameterized by the elliptic function, where the integrability condition is understood as the addition theorem of the elliptic function. The generalization of this integrability condition is to find the solution of the higher rank Lie group integrability condition and also to find the model parameterized by higher genus hyperelliptic function. For the preparation of this purpose, we give the explicit formula of the addition formula for g = 2 hyperelliptic function.

math-ph↗

arXiv2019

The Static Elliptic $N$-soliton Solutions of the KdV Equation

Regarding $N$-soliton solutions, the trigonometric type, the hyperbolic type, and the exponential type solutions are well studied. While for the elliptic type solution, we know only the one-soliton solution so far. Using the commutative Bäcklund transformation, we have succeeded in constructing the KdV static elliptic $N$-soliton solution, which means that we have constructed infinitely many solutions for the $\wp$-function type differential equation.

math-ph↗

arXiv2019

The Construction of the mKdV Cyclic Symmetric $N$-soliton Solution by the Bäcklund Transformation

We study group theoretical structures of the mKdV equation. The Schwarzian type mKdV equation has the global Möbius group symmetry. The Miura transformation makes a connection between the mKdV equation and the KdV equation. We find the special local Möbius transformation on the mKdV one-soliton solution which can be regarded as the commutative KdV Bäcklund transformation can generate the mKdV cyclic symmetric $N$-soliton solution. In this algebraic construction to obtain multi-soliton solutions, we could observe the addition formula.

nlin.SI↗

arXiv2017

Metric derived from Lie Groups

We give the expression of the metric derived from Lie groups. For the metric derived from classical Lie groups such as the unitary group, the orthogonal group and the symplectic group, we conjecture that the metric becomes the Einstein metric.

math.DG↗

arXiv2016

Zero, Normal and Super-radiant Modes for Scalar and Spinor Fields in Kerr-anti de Sitter Spacetime

Zero and normal modes for scalar and spinor fields in Kerr-anti de Sitter spacetime are studied as bound state problem with Dirichlet and Neumann boundary conditions. Zero mode is defined as the momentum near the horizon to be zero: $p_{\rm H}=ω-Ω_{\rm H}m=0$, and is shown not to exist as physical state for both scalar and spinor fields. Physical normal modes satisfy the spectrum condition $p_{\rm H}>0$ as a result of non-existence of zero mode and the analyticity with respect to rotation parameter $a$ of Kerr-anti de Sitter black hole. Comments on the super-radiant modes and the thermodynamics of black hole are given in relation to the spectrum condition for normal modes. Preliminary numerical analysis on normal modes is presented.

gr-qc↗

arXiv2013

The Elliptic Function in Statistical Integrable Models II

Two dimensional statistical integrable models, such as the Ising model, the chiral Potts model and the Belavin model, becomes integrable. Because of the SU(2) symmetry of these models, these models become integrable. The integral models are often parameterized by the elliptic function or the elliptic theta function. In this paper, we study the Ising model, and we show that the Yang-Baxter equation of the Ising model can be written as the integrability condition of SU(2), and we gives the natural explanation why the Ising model can be parameterized by the elliptic function by connecting the spherical trigonometry relation and the elliptic function. Addition formula of the elliptic function is the secret of the exact solvability of the Ising model.

math-ph↗

arXiv2008

Eigenvalue Problem of Scalar Fields in BTZ Black Hole Spacetime

We studied the eigenvalue problem of scalar fields in the (2+1)-dimensional BTZ black hole spacetime. The Dirichlet boundary condition at infinity and the Dirichlet or the Neumann boundary condition at the horizon are imposed. Eigenvalues for normal modes are characterized by the principal quantum number $(0<n)$ and the azimuthal quantum number $(-\infty<m< \infty)$. Effects to eigenvalues of the black hole rotation and of the scalar field mass are studied explicitly. Relation of the black hole rotation to the super-radiant instability is discussed.

gr-qc↗

arXiv2005

Comment on the Ghost State in the Lee Model

We examine the ghost state in the Lee model, and give the physically meaningful interpretatation for norm of the ghost state. According to this interpretation, the semi-positivity of the norm is guaranteed.

quant-ph↗

arXiv2005

Comment on the Origin of the Supermassive Black Hole

We give the comment why the supermassive black hole exists at the center of almost all galaxies. We consider the origin of the supermassive black hole from the point of view of the density of the matter. If the density of the matter is fixed and such matter can come together by the gravitational attraction, such stellar object eventually becomes the black hole. If the density of the matter is that of the atom, such matter naturally comes together to form the black hole by the gravitational attraction. This is expected to be the process to form the supermassive black hole. In this way, we can understand that there exists supermassive black hole at the center of almost all galaxies, because there is no delicate process to evolve into the black hole.

astro-ph↗

arXiv1994

Relation between Yang-Baxter and Pair Propagation Equations in 16-Vertex Models

We study a relation between two integrability conditions, namely the Yang-Baxter and the pair propagation equations, in 2D lattice models. While the two are equivalent in the 8-vertex models, discrepancies appear in the 16-vertex models. As explicit examples, we find the exactly solvable 16-vertex models which do not satisfy the Yang-Baxter equations.

hep-th↗

arXiv1992

Generalized Einstein Theory on Solar and Galactic Scales

We study a generalized Einstein theory with the following two criteria:{\it i}) on the solar scale, it must be consistent with the classical tests of general relativity, {\it ii}) on the galactic scale, the gravitational potential is a sum of Newtonian and Yukawa potentials so that it may explain the flat rotation curves of spiral galaxies. Under these criteria, we find that such a generalized Einstein action must include at least one scalar field and one vector field as well as the quadratic term of the scalar curvature.

astro-ph↗

arXiv1991

One-Point Functions of Loops and Constraints Equations of the Multi-Matrix Models at finite N

We derive one-point functions of the loop operators of Hermitian matrix-chain models at finite $N$ in terms of differential operators acting on the partition functions. The differential operators are completely determined by recursion relations from the Schwinger-Dyson equations. Interesting observation is that these generating operators of the one-point functions satisfy $W_{1+\infty}$-like algebra. Also, we obtain constraint equations on the partition functions in terms of the differential operators. These constraint equations on the partition functions define the symmetries of the matrix models at off-critical point before taking the double scaling limit.

hep-th↗