2018/12/11 by Takashi Yanagisawa · 3 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Asymptotic freedom #Beta function (physics) #Black Holes and Theoretical Physics #Functional renormalization group #Hyperbolic function #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Nonlinear system #Normalization (sociology) #Physics #Quantum electrodynamics #Quantum gravity #Quantum mechanics #Regularization (linguistics) #Renormalization #Renormalization group #Sine #Soliton #Thermal quantum field theory #cond-mat.stat-mech #hep-th #sine-Gordon equation
paper · pdf · doi:10.1093/ptep/pty141
published in Progress of Theoretical and Experimental Physics 2019(2) (University of Oxford) · 6 pages, 4 figures
openalex publication_date 2018/12/11 · arxiv created 2019/02/20 · arxiv updated 2019/02/21 · openalex created_date 2019/02/21 · openalex updated_date 2026/08/05
We present a renormalization group analysis for the hyperbolic sine-Gordon (sinh-Gordon) model in two dimensions. We derive the renormalization group equations based on the dimensional regularization method and the Wilson method. The same equations are obtained using both these methods. We have two parameters, |α| and |β≡ √(t)|, where |α| indicates the strength of interaction of a real salar field and |t=β2| is related to the normalization of the action. We show that |α| is renormalized to zero in the high-energy region; that is, the sinh-Gordon theory is an asymptotically free theory. We also show a non-renormalization property that the beta function of |t| vanishes in two dimensions.