Semiclassical Scaling Functions of Sine--Gordon Model

Details Semiclassical Scaling Functions of Sine--Gordon Model Semiclassical Scaling Functions of Sine--Gordon Model

2004-05-16

arxiv.org/abs/hep-th/0405139v1

Nucl.Phys. B699 (2004) 545-574

Physics

High Energy Physics

High Energy Physics - Theory

33 pages, 6 figures

Scientific paper

10.1016/j.nuclphysb.2004.08.004

We present an analytic study of the finite size effects in Sine--Gordon model, based on the semiclassical quantization of an appropriate kink background defined on a cylindrical geometry. The quasi--periodic kink is realized as an elliptic function with its real period related to the size of the system. The stability equation for the small quantum fluctuations around this classical background is of Lame' type and the corresponding energy eigenvalues are selected inside the allowed bands by imposing periodic boundary conditions. We derive analytical expressions for the ground state and excited states scaling functions, which provide an explicit description of the flow between the IR and UV regimes of the model. Finally, the semiclassical form factors and two-point functions of the basic field and of the energy operator are obtained, completing the semiclassical quantization of the Sine--Gordon model on the cylinder.

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