The boundary sine-Gordon theory: classical and semi-classical analysis
نویسندگان
چکیده
We consider the sine-Gordon model on a half-line, with an additional potential term of the form −M cos β2 (φ − φ0) at the boundary. We compute the classical time delay for general values of M , β and φ0 using τ -function methods and show that in the classical limit, the method of images still works, despite the non-linearity of the problem. We also perform a semi-classical analysis, and find agreement with the exact quantum S-matrix conjectured by Ghoshal and Zamolodchikov.
منابع مشابه
Generalized solution of Sine-Gordon equation
In this paper, we are interested to study the Sine-Gordon equation in generalized functions theory introduced by Colombeau, in the first we give result of existence and uniqueness of generalized solution with initial data are distributions (elements of the Colombeau algebra). Then we study the association concept with the classical solution.
متن کاملIntegrable boundary conditions for classical sine-Gordon theory
The possible boundary conditions consistent with the integrability of the classical sine-Gordon equation are studied. A boundary value problem on the half-line x ≤ 0 with local boundary condition at the origin is considered. The most general form of this boundary condition is found such that the problem be integrable. For the resulting system an infinite number of involutive integrals of motion...
متن کاملOn Duality and Reflection Factors for the Sinh-gordon Model with a Boundary
The sinh-Gordon model with integrable boundary conditions is considered in low order perturbation theory. It is pointed out that results obtained by Ghoshal for the sine-Gordon breather reflection factors suggest an interesting dual relationship between models with different boundary conditions. Ghoshal's formula for the lightest breather is checked perturbatively to O(β 2) in the special set o...
متن کاملSolving Some Initial-Boundary Value Problems Including Non-classical Cases of Heat Equation By Spectral and Countour Integral Methods
In this paper, we consider some initial-boundary value problems which contain one-dimensional heat equation in non-classical case. For this problem, we can not use the classical methods such as Fourier, Laplace transformation and Fourier-Birkhoff methods. Because the eigenvalues of their spectral problems are not strictly and they are repeated or we have no eigenvalue. The presentation of the s...
متن کاملFree Vibration Analysis of Variable Stiffness Composite Laminates with Flat and Folded Shapes
In this article, free vibration analysis of variable stiffness composite laminate (VSCL) plates with flat and folded shapes is studied. In order to consider the concept of variable stiffness, in each layer of these composite laminated plates, the curvilinear fibers are used instead of straight fibers. The analysis is based on a semi-analytical finite strip method which follows classical laminat...
متن کامل