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Takao Koikawa

Publications and source records attributed to Takao Koikawa.

At least 19 recordsLinked to original sources
arXiv2026

Gauge-Theoretical Method in Solving Zero-curvature Equations III --Gauge Theoretical Method and the Bäcklund Transformations for Solitons--

In soliton theory, both the gauge-theoretical method and the Bäcklund transformation yield soliton equations from the compatibility condition of a pair of linear equations. Therefore, it is necessary to clarify the similarities and differences between these two methods. The Bäcklund transformation defines a transformation from one soliton solution to another. In particular, restricting the transformation to solutions with different soliton numbers yields interesting insights. Using several examples, we demonstrate how soliton solutions with different soliton numbers are constructed.

hep-th↗
arXiv2025

Gauge-Theoretical Method in Solving Zero-curvature Equations II--Non-Weyl Class Solutions of the Static Einstein-Maxwell Equations

The gauge-theoretical method introduced in our previous paper is applied to solve the axisymmetric and static Einstein-Maxwell equations. We obtain the solutions of the non-Weyl class, where the gravitational and electric or magnetic potentials are not functionally related. In the electrostatic case, we show that the obtained solution coincides with the solution given by Bonnor in 1979. In the magnetostatic case, we present a solution describing the gravitational field created by two magnetically charged masses. In this solution, we present a case in which the Dirac string does not stretch to spatial infinity but lies between the magnetically charged masses.

gr-qc↗
arXiv2025

Gauge Theoretical Method in Solving Zero-curvature Equations I. -- Application to the Static Einstein-Maxwell Equations with Magnetic Charge

The inverse scattering problem is applied to 2-dimensional partial differential equations called soliton equations such as the KdV equation and so on. It is also used to integrate the Einstein equations with axial symmetry. These inverse scattering problems look different. We show that they can be understood in a unified way. As an application to the Einstein equation, we find solutions of the Einstein-Maxwell equations with a magnetic charge.

hep-th↗
arXiv2010

Lie Algebra Quantization by the Star Product

We apply the star product quantization to the Lie algebra. The quantization in terms of the star product is well known and the commutation relation in this case is called the $θ$-deformation where the constant $θ$ appears as a parameter. In the application to the Lie algebra, we need to change the parameter $θ$ to $x$-dependent $θ(x)$. There is no essential difference between the quantization in the quantum mechanics and deriving quantum numbers in the Lie algebra from the viewpoint of the star product. We propose to unify them in higher dimensions, which may be analogous to the Kaluza-Klein theory in the classical theory.

hep-th↗
arXiv2007

An Infinite Number of Static Soliton Solutions to 5D Einstein-Maxwell Equations

The soliton technique is applied to the 5D static Einstein-Maxwell equations, and an infinite number of solutions are explicitly obtained. We study the rod structure of 2-soliton solutions and we show that the 5D Reissner-Nordstrom solution and the 5D Majumdar-Papapetrou solution are included as the 2-soliton solutions.

hep-th↗
arXiv2005

Infinite Number of Stationary Soliton Solutions to Five-dimensional Vacuum Einstein Equation

We obtain an infinite number of soliton solutions to the the five-dimensional stationary Einstein equation with axial symmetry by using the inverse scattering method. We start with the five-dimensional Minkowski space as a seed metric to obtain these solutions. The solutions are characterized by two soliton numbers and a constant appearing in the normalization factor related to a coordinate condition. We show that the (2,0)-soliton solution is identical to the Myers-Perry solution with one angular momentum by imposing a condition between parameters. We also show that the (2,2)-soliton solution is different from the black ring solution discovered by Emparan and Reall, although one component of the metric of two metrics can be identical.

hep-th↗
arXiv2005

Infinite number of soliton solutions to 5-dimensional vacuum Einstein equation

We give an infinite number of exact solutions to the 5-dimensional static Einstein equation with axial symmetry by using the inverse scattering method. The solutions are characterized by two integers representing the soliton numbers. The first non trivial example of these solutions is the static black ring solution found recently.

hep-th↗
arXiv2004

Moyal Quantization on Fuzzy Sphere

We study the quantization of compact space on the basis of the Moyal quantization. We first construct the $su(2)$ algebra that are the functions of canonical coordinates $a$ and $a^*$. We make use of them to define the adjoint operators, which is used to define the fuzzy sphere and constitute the algebra. We show that the vacuum is constructed as the powers of $a^*$, in contrast to the flat case where the vacuum is defined by the exponential function of $a$ and $a^*$. We present how the analogy of the creation operator acting on the vacuum is obtaied. The construction does not resort to the ordinary creation and annihilation operators.

hep-th↗
arXiv2003

Quantization via Star Products

We study quantization via star products. We investigate a quantization scheme in which a quantum theory is described entirely in terms of the function space without reference to a Hilbert space, unlike the formulation employing the Wigner functions. The associative law plays an essential role in excluding the unwanted solutions to the stargen-value equation. This is demonstrated explicitly with the $D$-dimensional harmonic oscillator.

hep-th↗
arXiv2002

Moyal Quantization for Constrained System

We study the Moyal quantization for the constrained system. One of the purposes is to give a proper definition of the Wigner-Weyl(WW) correspondence, which connects the Weyl symbols with the corresponding quantum operators. A Hamiltonian in terms of the Weyl symbols becomes different from the classical Hamiltonian for the constrained system, which is related to the fact that the naively constructed WW correspondence is not one-to-one any more. In the Moyal quantization a geometrical meaning of the constraints is clear. In our proposal, the 2nd class constraints are incorporated into the definition of the WW correspondence by limiting the phasespace to the hypersurface. Even though we assume the canonical commutation relations in the formulation, the Moyal brackets between the Weyl symbols yield the same results as those for the constrained system derived by using the Dirac bracket formulation.

hep-th↗
arXiv2001

Role of the imaginary part in the Moyal quantization

We show that the imaginary part of the $\star$-genvalue equation in the Moyal quantization reveals the symmetries of the Hamiltonian by which we obtain the conserved quantities. Applying to the Toda lattice equation, we derive conserved quantities which are used as the independent variables of Wigner function.

hep-th↗
arXiv2001

On the vacuum in the Moyal quantization

We study the features of the vacuum of the harmonic oscillator in the Moyal quantization. The vacuums with and without using the normal ordering look different. The vacuum without the normal ordering is shown to be expressed using the Weyl ordering. The Weyl ordered vacuum is then compared with the normal ordered vacuum, and the implication of the difference between them is discussed.

hep-th↗
arXiv2001

Soliton Equations Extracted from the Noncommutative Zero-Curvature Equation

We investigate the equation where the commutation relation in 2-dimensional zero-curvature equation composed of the algebra-valued potentials is replaced by the Moyal bracket and the algebra-valued potentials are replaced by the non-algebra-valued ones with two more new variables. We call the 4-dimensional equation the noncommutative zero-curvature equation. We show that various soliton equations are derived by the dimensional reduction of the equation.

hep-th↗
arXiv1999

Soliton formulation by Moyal algebra

We formulate the soliton equations on the lattice in terms of the reduced Moyal algebra which includes one parameter. The vanishing limit of the parameter leads to the continuous soliton equations.

hep-th↗
arXiv1998

Discrete and Continuous Bogomolny Equations through the Deformed Algebra

We connect the discrete and continuous Bogomolny equations. There exists one-parameter algebra relating two equations which is the deformation of the extended conformal algebra. This shows that the deformed algebra plays the role of the link between the matrix valued model and the model with one more space dimension higher.

hep-th↗
arXiv1997

Magnetic solutions to 2+1 dimensional gravity with dilaton field

We show a general method to solve 2+1 dimensional dilatonic Maxwell-Einstein equation with a positive or negative cosmological constant. All the physical solutions are listed with assumptions that they are static, rotationally symmetric, and has a nonzero magnetic field and a nonzero dilaton field. On the contrary to the magnetic solution without a dilaton field, some of the present solutions with a dilaton field possess a horizon.

hep-th↗