On the renormalization of the sine–Gordon model

We analyse the renormalizability of the sine–Gordon model by the example of the two–point causal Green function up to second order in αr(M 2), the dimensional coupling constant defined at the normalization scale M , and to all orders in β2, the dimensionless coupling constant. We show that all divergences can be removed by the renormalization of the dimensional coupling constant using the renormalization constant Z1, calculated in (J. Phys. A 36, 7839 (2003)) within the path–integral approach. We show that after renormalization of the two–point Green function to first order in αr(M 2) and to all orders in β2 all higher order corrections in αr(M 2) and arbitrary orders in β2 can be expressed in terms of αph, the physical dimensional coupling constant independent on the normalization scaleM . We calculate the Gell– Mann–Low function and analyse the dependence of the two–point Green function on αph and the running coupling constant within the Callan–Symanzik equation. We analyse the renormalizability of Gaussian fluctuations around a soliton solution. We show that Gaussian fluctuations around a soliton solution are renormalized like quantum fluctuations around the trivial vacuum to first orders in αr(M 2) and β2 and do not introduce any singularity to the sine–Gordon model at β2 = 8π. The finite correction to the soliton mass, coinciding with that calculated by Dashen et al. (Phys. Rev. D 10, 4130 (1974)), appears in our approach to second order in αph and to first order in β2. This is a perturbative correction, which provides no singularity for the sine–Gordon model at β2 = 8π. We calculate the correction to the soliton mass, caused by Gaussian fluctuations around a soliton, within the discretization procedure for various boundary conditions and find complete agreement with our result, obtained in continuous space–time. PACS: 11.10.Ef, 11.10.Gh, 11.10.Hi, 11.10.Kk E–mail: [email protected], Tel.: +43–1–58801–14262, Fax: +43–1–58801–14299 E–mail: [email protected], Tel.: +43–1–58801–14261, Fax: +43–1–58801–14299 E–mail: [email protected], Tel.: +43–1–58801–14261, Fax: +43–1–58801–14299 Permanent Address: State Polytechnic University, Department of Nuclear Physics, 195251 St. Petersburg, Russian Federation E–mail: [email protected], Tel.: +43–1–58801–14263, Fax: +43–1–58801–14299 1