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 analysis of superradiant growth of self-interacting axion cloud

2021 ◽  
Author(s):  
Hidetoshi Omiya ◽  
Takuya Takahashi ◽  
Takahiro Tanaka
Keyword(s):  
Black Hole ◽  
Renormalization Group ◽  
Scalar Field ◽  
Group Analysis ◽  
Group Method ◽  
Renormalization Group Method ◽  
Renormalization Group Analysis ◽  
Rotating Black Hole ◽  
Realistic Situation ◽  
Light Scalar

Abstract There are strong interests in considering the ultra-light scalar field (especially axion) around a rapidly rotating black hole because of the possibility of observing a gravitational waves from axion condensate (axion cloud) around black hole. Motivated by this consideration, we study dynamics of ultra-light scalar field with self-interaction around a rapidly rotating black hole by the Renormalization group method. We found that for the relativistic cloud, saturation of the superradiant instability by the scattering of the axion due to the self-interaction does not occur in the weakly non-linear regime. This means that for the relativistic axion cloud, explosive phenomena called the Bosenova might happen in the realistic situation.

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.

scholarly journals QUANTUM ELECTRODYNAMICS AND CHROMODYNAMICS TREATED THROUGH THOMPSON'S APPROACH

2006 ◽  
Vol 21 (18) ◽  
pp. 3809-3824 ◽  
Author(s):  
CLÁUDIO NASSIF ◽  
P. R. SILVA
Keyword(s):  
Quantum Electrodynamics ◽  
Heuristic Method ◽  
Critical Dimension ◽  
Step Function ◽  
Quark Condensate ◽  
Energy Scale ◽  
Field Theories ◽  
Coupling Constant ◽  
Running Coupling ◽  
Running Coupling Constant

In this work we apply Thompson's method (of the dimensions and scales) to study some features of the Quantum Electrodynamics and Chromodynamics. This heuristic method can be considered as a simple and alternative way to the Renormalization Group approach and when applied to QED-Lagrangian is able to obtain in a first approximation both the running coupling constant behavior of α(μ) and the mass m(μ). The calculations are evaluated only at dc = 4, where dc is the upper critical dimension of the problem, so that we obtain the logarithmic behavior both for the coupling α and the excess of mass Δm on the energy scale μ. Although our results are well known in the vast literature of field theories, the advantage of Thompson's method, beyond its simplicity is that it is able to extract directly from QED-Lagrangian the physical (finite) behavior of α(μ) and m(μ), bypassing hard problems of divergences which normally appear in the conventional renormalization schemes applied to field theories like QED. Quantum Chromodynamics (QCD) is also treated by the present method in order to obtain the quark condensate value. Besides this, the method is also able to evaluate the vacuum pressure at the boundary of the nucleon. This is done by assumming a step function behavior for the running coupling constant of the QCD, which fits nicely to some quantities related to the strong interaction evaluated through the MIT-bag model.

scholarly journals Monte Carlo and renormalization-group effective potentials in scalar field theories

1995 ◽  
Vol 51 (12) ◽  
pp. 7017-7025 ◽  
Author(s):  
J. R. Shepard ◽  
V. Dmitrašinović ◽  
J. A. McNeil
Keyword(s):  
Monte Carlo ◽  
Renormalization Group ◽  
Scalar Field ◽  
Field Theories ◽  
Effective Potentials

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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