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.Comment: 17 pages, 6 eps figure

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

Distance Formula for Grassmann Manifold --Applied to Anandan--Aharonov Type Uncertainty Relation--

The time-energy uncertainty relation of Anandan-Aharonov is generalized to a relation involving a set of quantum state vectors. This is achieved by obtaining an explicit formula for the distance between two finitely separated points in the Grassmann manifold.Comment: 25pages, LaTex file , TOYAMA-80, KANAZAWA-94-2

Induced Gauge Structure of Quantum Mechanics on SDS^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.Comment: LaTex,15Page

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.Comment: 8 page

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.Comment: 9pages,4figure

Generalization of the Time-Energy Uncertainty Relation of Anandan-Aharonov Type

A new type of time-energy uncertainty relation was proposed recently by Anandan and Aharonov. Their formula, to estimate the lower bound of time-integral of the energy-fluctuation in a quantum state is generalized to the one involving a set of quantum states. This is achieved by obtaining an explicit formula for the distance between two finitely separated points in the Grassman manifold

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.Comment: 11 pages, 2 figure