2005/05/31 by H. Bozkaya, M. Faber, Bozkaya, H. +6 · 1 citation
Mathematics · Physics and Astronomy · #Nonlinear Waves and Solitons #hep-lat #hep-ph #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.hep-th/0505276
33 pages, 2 figures
arxiv created 2005/05/31 · arxiv updated 2009/12/01
We analyse the renormalizability of the sine-Gordon model by the example of the two-point Green function up to second order in alphar(M), the dimensional coupling constant defined at the normalization scale M, and to all orders in beta2, 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.A36,7839(2003)) within the path-integral approach. We show that after renormalization of the two-point Green function to first order in alphar(M) and to all orders in beta2 all higher order corrections in alphar(M) and arbitrary orders in beta2 can be expressed in terms of alphaph, the physical dimensional coupling constant independent on the normalization scale M. We solve the Callan-Symanzik equation for the two-point Green function. 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 alphar(M) and beta2 and do not introduce any singularity to the sine-Gordon model at beta2 = 8pi.