Naohisa Ogawa

A Note on classical solution of Chaplygin gas as d-branes

The classical solution of a bosonic d-brane in

Surface instability of icicles

(d+1,1)

Quantum Mechanics in Riemannian Manifold. II

space-time is studied. We work with the light-cone gauge and reduce the problem into a Chaplygin gas problem. The static equation is equivalent to the vanishing of the extrinsic mean curvature, which is similar to Einsteins equation in vacuum. We show that the d-brane problem in this gauge is closely related to the plateau problem, and we give some nontrivial solutions from minimal surfaces. The solutions of

Curvature-dependent diffusion flow on a surface with thickness

d\ensuremath{-}1,d,d+1

Geometrically Induced Gauge Structure on Manifolds Embedded in a Higher Dimensional Space

spatial dimensions are obtained from d-dimensional minimal surfaces as solutions of the plateau problem. In addition we discuss the relation to the Hamiltonian-BRST formalism for d-branes.

On the rotating soliton in the Chiral model

Quantitatively unexplained stationary waves or ridges often encircle icicles. Such waves form when roughly 0.1-mm-thick layers of water flow down an icicle. These waves typically have a wavelength of about 1 cm, which is independent of external temperature, icicle thickness, and the volumetric rate of water flow. In this paper, we show that these waves cannot be obtained by a naive Mullins-Sekerka instability but are caused by a quite different type of surface instability related to thermal diffusion and the hydrodynamic effect of a thin water flow.

The Difference of Effective Hamiltonian in Two Methods in Quantum Mechanics on Submanifold

We have previously argued about the quantum mechanics on the hypersurface V N−1 embedded in Euclidean space R N . We generalize the formalism to the case of V L embedded in Euclidean space R N with 1≤L≤N. The result is essentially the same as the previous one and the additional term proportional to h 2 appears in the potential energy which is related to the extrinsic mean curvature of V L in R N

Generalization of Geometry-Induced Gauge Structure to Any Dimensional Manifold

Particle diffusion in a two-dimensional curved surface embedded in R3 is considered. In addition to the usual diffusion flow, we find a flow with an explicit curvature dependence. Diffusion equation is obtained in ϵ (thickness of surface) expansion. As an example, the surface of elliptic cylinder is considered, and curvature-dependent diffusion coefficient is calculated.

A Note on Gauge Principle and Spontaneous Symmetry Breaking in Classical Particle Mechanics

We explain in a context different from that of Maraner the formalism for describing the motion of a particle, under the influence of a confining potential, in a neighborhood of an n-dimensional curved manifold Mn embedded in a p-dimensional Euclidean space Rp with p ≥ n + 2. The effective Hamiltonian on Mn has a (generally non-Abelian) gauge structure determined by the geometry of Mn. Such a gauge term is defined in terms of the vectors normal to Mn, and its connection is called the N connection. This connection is nothing but the connection induced from the normal connection of the submanifold Mn of Rp. In order to see the global effect of this type of connections, the case of M1 embedded in R3 is examined, where the relation of an integral of the gauge potential of the N connection (i.e. the torsion) along a path in M1 to the Berry phase is given through Gauss mapping of the vector tangent to M1. Through the same mapping in the case of M1 embedded in Rp, where the normal and the tangent quantities are exchanged, the relation of the N connection to the induced gauge potential (the canonical connection of the second kind) on the (p - 1)-dimensional sphere Sp - 1 (p ≥ 3) found by Ohnuki and Kitakado is concretely established; the former is the pullback of the latter by the Gauss mapping. Further, this latter which has the monopole-like structure is also proved to be gauge-equivalent to the spin connection of Sp - 1. Thus the N connection is also shown to coincide with the pullback of the spin connection of Sp - 1. Finally, by extending formally the fundamental equations for Mn to the infinite-dimensional case, the present formalism is applied to the field theory that admits a soliton solution. The resultant expression is in some respects different from that of Gervais and Jevicki.

Chapter I Quantization of Chiral Solitons in Collective .. Coordinate Approach

We study the quantum rotating soliton in the nonlinear σ model which is obtained by minimizing the total energies of rotating soliton. Existence of such a soliton is expected from the Derrick’s theorem even when the Skyrme term is absent because the rotational energy prevents the soliton from collapsing. The asymptotic behavior of the profile function is shown to be determined by the physical pion mass which appears in the PCAC relation in the nonlinear σ model. The energies of spin-1/2 and − 3/2 solitons are obtained numerically with the use of a simple trial function.