scholarly journals Derivative expansion of the effective action and the renormalization group equation

2007 ◽  
Vol 76 (10) ◽  
Author(s):  
F. A. Chishtie ◽  
Junji Jia ◽  
D. G. C. McKeon
Keyword(s):  
Renormalization Group ◽  
Effective Action ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Derivative Expansion

RENORMALIZATION GROUP EQUATION AND EFFECTIVE ACTION IN STRING THEORY

1989 ◽  
Vol 04 (10) ◽  
pp. 941-951 ◽  
Author(s):  
J. GAITE
Keyword(s):  
Renormalization Group ◽  
String Theory ◽  
Effective Action ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Generating Functional ◽  
S Matrix

The connection between the renormalization group for the σ-model effective action for the Polyakov string and the S-matrix generating functional for dual amplitudes is studied. A more general approach to the renormalization group equation for string theory is proposed.

scholarly journals Exact Renormalization Group Approach in Scalar and Fermionic Theories

1998 ◽  
Vol 12 (12n13) ◽  
pp. 1321-1341 ◽  
Author(s):  
Yu. Kubyshin
Keyword(s):  
Perturbation Theory ◽  
Renormalization Group ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Derivative Expansion ◽  
Group Approach ◽  
Renormalization Group Approach ◽  
Exact Renormalization Group

The Polchinski version of the exact renormalization group equation is discussed and its applications in scalar and fermionic theories are reviewed. Relation between this approach and the standard renormalization group is studied, in particular the relation between the derivative expansion and the perturbation theory expansion is worked out in some detail.

scholarly journals Quantum Fields without Wick Rotation

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 373 ◽  
Author(s):  
Alessio Baldazzi ◽  
Roberto Percacci ◽  
Vedran Skrinjar
Keyword(s):  
Renormalization Group ◽  
Effective Action ◽  
Coarse Graining ◽  
Conformal Factor ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Simple Application ◽  
Wick Rotation ◽  
Definition Of ◽  
Method Of Steepest Descent

We discuss the calculation of one-loop effective actions in Lorentzian spacetimes, based on a very simple application of the method of steepest descent to the integral over the field. We show that for static spacetimes this procedure agrees with the analytic continuation of Euclidean calculations. We also discuss how to calculate the effective action by integrating a renormalization group equation. We show that the result is independent of arbitrary choices in the definition of the coarse-graining and we see again that the Lorentzian and Euclidean calculations agree. When applied to quantum gravity on static backgrounds, our procedure is equivalent to analytically continuing time and the integral over the conformal factor.

scholarly journals Renormalization group and diffusion equation

2020 ◽  
Author(s):  
Masami Matsumoto ◽  
Gota Tanaka ◽  
Asato Tsuchiya
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Diffusion Equation ◽  
Effective Action ◽  
Renormalization Group Equation ◽  
Initial Time ◽  
Group Equation ◽  
Cutoff Function ◽  
Exact Renormalization Group ◽  
And Diffusion

Abstract We study relationship between renormalization group and diffusion equation. We consider the exact renormalization group equation for a scalar field that includes an arbitrary cutoff function and an arbitrary quadratic seed action. As a generalization of the result obtained by Sonoda and Suzuki, we find that the correlation functions of diffused fields with respect to the bare action agree with those of bare fields with respect to the effective action, where the diffused field obeys a generalized diffusion equation determined by the cutoff function and the seed action and agrees with the bare field at the initial time.

scholarly journals Effective action from the functional renormalization group

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
Nobuyoshi Ohta ◽  
Lesław Rachwał
Keyword(s):  
Renormalization Group ◽  
Effective Action ◽  
Flow Equation ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Dirac Fermions ◽  
Charged Scalar ◽  
Functional Renormalization Group ◽  
Scale Down ◽  
Nonlocal Terms

AbstractWe study the quantum gravitational system coupled to a charged scalar, Dirac fermions, and electromagnetic fields. We use the “exact” or “functional” renormalization group equation to derive the effective action $$\Gamma _0$$ Γ 0 by integrating the flow equation from the ultraviolet scale down to $$k=0$$ k = 0 . The resulting effective action consists of local terms and nonlocal terms with unique coefficients.

EXTERNAL FIELDS AND THE RENORMALIZATION GROUP

1988 ◽  
Vol 03 (07) ◽  
pp. 661-666
Author(s):  
T. E. CLARK ◽  
S. T. LOVE
Keyword(s):  
Magnetic Field ◽  
Renormalization Group ◽  
External Magnetic Field ◽  
External Field ◽  
Field Dependence ◽  
Effective Action ◽  
Renormalization Group Equation ◽  
The Other ◽  
Group Equation ◽  
Scaling Arguments

Scaling arguments are used to relate the external field dependence of the vacuum functional to the changes in the other parameters characterizing the model. Under certain circumstances, this renormalization group equation can be solved, at least approximately, for the external field dependence of the effective action. In particular, we focus on the case of a strong external magnetic field.

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