Semiclassical Scaling Functions of Sine--Gordon Model

TL;DR

This paper provides an analytical semiclassical analysis of finite size effects in the Sine--Gordon model, deriving explicit scaling functions and form factors that describe the model's behavior across different energy regimes.

Contribution

It introduces a novel semiclassical approach to compute scaling functions and form factors in the Sine--Gordon model on a cylindrical geometry, connecting IR and UV regimes.

Findings

Derived explicit ground state and excited state scaling functions.

Obtained semiclassical form factors and two-point functions.

Described the flow between IR and UV regimes.

Abstract

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.