Renormalization group method for kink dynamics in a perturbed sine-Gordon equation

2014 ◽  
Vol 28 (09) ◽  
pp. 1450068 ◽  
Author(s):  
Li Wang ◽  
Tao Tu ◽  
Ping-Guo Guo ◽  
Guang-Can Guo
Keyword(s):  
Renormalization Group ◽  
Scattering Theory ◽  
Present Method ◽  
Gordon Equation ◽  
Group Method ◽  
Renormalization Group Theory ◽  
Renormalization Group Method ◽  
Sine Gordon Equation ◽  
Soliton Dynamics ◽  
Insight Into

In this paper, we show that renormalization group theory can be used to give a systematic description of the evolution of the kink in a perturbed sine-Gordon equation. The present method gives the same results as inverse scattering theory and other approaches, which may provide a new insight into the soliton dynamics of perturbed equations.

UNIFIED TREATMENT OF THE SCALAR FIELD THEORIES-Φn THROUGH THOMPSON'S RENORMALIZATION GROUP METHOD

2003 ◽  
Vol 17 (26) ◽  
pp. 4645-4660 ◽  
Author(s):  
CLÁUDIO NASSIF ◽  
P. R. SILVA
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Present Method ◽  
Critical Dimension ◽  
Energy Scale ◽  
Field Theories ◽  
Group Method ◽  
Renormalization Group Method ◽  
Coupling Constant ◽  
Upper Critical Dimension

In this work we apply Thompson's scaling approach (of dimensions) to study the scalar field theories Φn. This method can be considered as a simple and alternative way to the renormalization group (RG) approach and when applied to the Φn Lagrangian is able to obtain the coupling constant behavior g(μ), namely the dependence of g on the energy scale μ. The calculations are evaluated just at [Formula: see text], where the dimension dc is similar to a kind of upper critical dimension of the problem, or in other words the dimension where the Φn theory becomes renormalizable, so that we obtain logarithmic behavior of the coupling g at dc. Due to the universal logharithmic behavior of the coupling g at dc for any value of n in the Φn theory, we are able to estimate a certain βn function given in a closed form, which is a novelty obtained by the present method.

scholarly journals Renormalization group theory of the generalized multi-vertex sine-Gordon model

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Takashi Yanagisawa
Keyword(s):  
Renormalization Group ◽  
Group Theory ◽  
Regularization Method ◽  
Dimensional Regularization ◽  
Group Method ◽  
Regular Tetrahedron ◽  
Renormalization Group Theory ◽  
Renormalization Group Method ◽  
Triangle Condition ◽  
Sine Gordon Model

Abstract We investigate the renormalization group theory of the generalized multi-vertex sine-Gordon model by employing the dimensional regularization method and also the Wilson renormalization group method. The vertex interaction is given by $\cos(k_j\cdot \phi)$, where $k_j$ ($j=1,2,\ldots,M$) are momentum vectors and $\phi$ is an $N$-component scalar field. The beta functions are calculated for the sine-Gordon model with multiple cosine interactions. The second-order correction in the renormalization procedure is given by the two-point scattering amplitude for tachyon scattering. We show that new vertex interaction with the momentum vector $k_{\ell}$ is generated from two vertex interactions with vectors $k_i$ and $k_j$ when $k_i$ and $k_j$ meet the condition $k_{\ell}=k_i\pm k_j$, called the triangle condition. A further condition $k_i\cdot k_j=\pm 1/2$ is required within the dimensional regularization method. The renormalization group equations form a set of closed equations when $\{k_j\}$ form an equilateral triangle for $N=2$ or a regular tetrahedron for $N=3$. The Wilsonian renormalization group method gives qualitatively the same result for beta functions.

scholarly journals New applications of the renormalization group method in physics: a brief introduction

2011 ◽  
Vol 369 (1946) ◽  
pp. 2602-2611 ◽  
Author(s):  
Y. Meurice ◽  
R. Perry ◽  
S.-W. Tsai
Keyword(s):  
Renormalization Group ◽  
Phase Transitions ◽  
Dynamical Systems ◽  
Particle Physics ◽  
Recent Progress ◽  
Condensed Matter ◽  
Group Method ◽  
Renormalization Group Method ◽  
Theme Issue ◽  
New Applications

The renormalization group (RG) method developed by Ken Wilson more than four decades ago has revolutionized the way we think about problems involving a broad range of energy scales such as phase transitions, turbulence, continuum limits and bifurcations in dynamical systems. The Theme Issue provides articles reviewing recent progress made using the RG method in atomic, condensed matter, nuclear and particle physics. In the following, we introduce these articles in a way that emphasizes common themes and the universal aspects of the method.

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