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Minoru Hirayama

Publications and source records attributed to Minoru Hirayama.

13 recordsLinked to original sources
arXiv2012

Solitonic solutions of Faddeev model

An application of the equation proposed by the present authors, which is equivalent to the static field equation of the Faddeev model, is discussed. Under some assumptions on the space and on the form of the solution, the field equation is reduced to a non-linear ODE of second order. By solving this equation numerically, some solitonic solutions are obtained. It is discussed that the product of two integers specifying solutions may be identified with the Hopf topological invariant.

math-ph↗
arXiv2009

Cross-fertilization of Ferreira's Hopfions And Electromagnetic Knots

The interrelation between Ferreira's Hopf solitons of a conformal nonlinear $σ$ model and the electromagnetic knots found by Ra$\tilde{\rm{n}}$ada et al. is investigated. It is shown that the electromagnetic knots yield exact solutions of the conformal nonlinear $σ$ model different from those obtained by Ferreira. Conversely, It is discussed that Ferreira's solutions realize magnetic knots. The energy associated with these two kinds of knots are compared. The structure of the electric charge distribution and the electric current density associated with the magnetic knots is investigated.

hep-th↗
arXiv2007

Approximate vortex solution of Faddeev model

Through an Ansatz specifying the azimuthal-angle dependence of the solution, the static field equation for vortex of the Faddeev model is converted to an algebraic ordinary differential equation. An approximate analytic expression of the vortex solution is explored so that the energy per unit vortex length becomes as small as possible. It is observed that the minimum energy of vortex is approximately proportional to the integer which specifies the solution.

hep-th↗
arXiv2007

Reduction of static field equation of Faddeev model

A method to solve the static field equation of the Faddeev model is presented. For an special combination of the concerned field, we adopt a form which is compatible with the field equation and involves two arbitrary complex functions. As a result, the static field equation is reduced to a set of first order partial differential equations.

hep-th↗
arXiv2006

Restricting profile function of hedgehog Skyrmion

The profile function for the hedgehog Skyrmion is investigated. After discussing how the form of the profile function is restricted by the field equation, the s tatic energy is numerically calculated. It is found that the profile functions c onsidered here sometimes give the static energy smaller than previous ones.

hep-th↗
arXiv2006

Estimation of the Lin-Yang bound of the least static energy of the Faddeev model

Lin and Yang's upper bound E_Q <= cQ^(3/4) of the least static energy E_Q of the Faddeev model in a sector with a fixed Hopf index Q is investigated. By constructing an explicit trial configuration for the Faddeev field n, a possible value of the coefficient c is obtained numerically, which is much smaller than the value obtained quite recently by analytic discussions.

hep-th↗
arXiv2006

Domain wall solution of the Skyrme model

A class of domain-wall-like solutions of the Skyrme model is obtained analytically. They are described by the tangent hyperbolic function, which is a special limit of the Weierstrass $\wp$ function. The behavior of one of the two terms in the static energy density is like that of a domain wall. The other term in the static energy density does not vanish but becomes constant at the points far apart from the wall.

hep-th↗
arXiv2002

Nonlinear sigma models solvable by the Aratyn-Ferreira-Zimerman ansatz

Nonlinear sigma models compatible with the aratyn-Ferreira-Zimerman ansatz are discussed, the latter ansatz automatically leading to configurations with definite values of the Hopf index. These models are allowed to involve a weight factor which is a function of one of the toroidal coordinates. Depending on the choice of the weight factor, the field equation takes various forms. In one model with a special weight factor, the field equation turns out to be the fifth Painleve equation. This model suggests the existence of a knot soliton strictly confined in a finite spatial volume. Some other interesting cases are also discussed.

hep-th↗
arXiv1997

Non-Abelian Gauge Configuration with a Magnetic Field Concentrated at a Point

A specific SU(2) gauge configuration yielding a magnetic field concentrated at a point is investigated. Its relation to the Aharonov-Bohm gauge potential and its cohomological meaning in a three dimensional space are clarified. Quantum mechanics of a spinning particle in such a gauge configuration is briefly discussed.

hep-th↗
arXiv1997

Induced Gauge Structure of Quantum Mechanics on $S^D$

The Ohnuki-Kitakado (O-K) scheme of quantum mechanics on $S^D$ embedded in $R^{D+1}$ is investigated. Generators satisfying the O-K algebra are written down explicitly in term of the induced gauge potential. A direct method is developed to obtain the generators in covariant form. It is seen that there exists an induced gauge configuration which is trivial on $S^D$ but might cause a nontrivial physical effect in $R^{D+1}$. The relation of the O-K scheme to extended objects such as the 't Hooft-Polyakov monopole is discussed.

hep-th↗
arXiv1997

Fermion Representation of Quantum Group

The spinor representation of the quantum group $U_q(su(N))$ is given in terms of a set of fermion creation and annihilation operators. It is shown that the $q$-fermion operators introduced earlier can be identifi ed with the conventional fermion operators. Algebra homomorphisms mapping the fermion operators to their t ensor products are discussed. The relation of the coproduct of the quantum group to the above algebra homo morphisms is obtained.

q-alg↗