scholarly journals THE EFFECTIVE POTENTIAL IN THE MASSIVE $\phi_4^4$ MODEL

2007 ◽  
Vol 22 (01) ◽  
pp. 1-9 ◽  
Author(s):  
F. BRANDT ◽  
F. CHISHTIE ◽  
D. G. C. MCKEON
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Effective Potential ◽  
Quantum Electrodynamics ◽  
Renormalization Group Equation ◽  
Massless Scalar ◽  
Group Equation ◽  
Scalar Quantum ◽  
Text Model

By applying the renormalization group equation, it has been shown that the effective potential V in the massless [Formula: see text] model and in massless scalar quantum electrodynamics is independent of the scalar field. This analysis is extended here to the massive [Formula: see text] model, showing that the effective potential is independent of ϕ here as well.

APPROXIMATE CALCULATION OF THE N-LOOP EFFECTIVE POTENTIAL FOR LARGE FIELD VALUES THROUGH THE RENORMALIZATION GROUP EQUATION

1996 ◽  
Vol 11 (10) ◽  
pp. 805-813
Author(s):  
MURAT ÖZER
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Effective Potential ◽  
Approximate Calculation ◽  
Approximate Expression ◽  
Renormalization Group Equation ◽  
Large Field ◽  
Group Equation

The renormalization group equation is used to obtain an approximate expression for the N-loop effective potential VN(ϕ) for large values of an interacting scalar field ϕ. The expression thus obtained is valid when the leading logarithms are much larger than the nonleading ones.

RG IMPROVEMENT OF THE EFFECTIVE POTENTIAL AT FINITE TEMPERATURE

1996 ◽  
Vol 11 (28) ◽  
pp. 2259-2269 ◽  
Author(s):  
HISAO NAKKAGAWA ◽  
HIROSHI YOKOTA
Keyword(s):  
Renormalization Group ◽  
Effective Potential ◽  
Finite Temperature ◽  
Renormalization Group Equation ◽  
Effective Procedure ◽  
Coefficient Function ◽  
Group Equation ◽  
Leading Order ◽  
Effective Potentials ◽  
The One

We present a simple and effective procedure to improve the finite temperature effective potential so as to satisfy the renormalization group equation (RGE). With the L-loop knowledge of the effective potential and of the RGE coefficient function, this procedure carries out a systematic resummation of large-T as well as large-log terms up to the Lth-to-leading order, giving an improved effective potential which satisfies the RGE and is exact up to the Lth-to-leading T and log terms. Applications to the one- and two-loop effective potentials are explicitly performed.

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 Commutative–non-commutative dualities

2020 ◽  
Vol 98 (2) ◽  
pp. 158-166
Author(s):  
F.G. Scholtz ◽  
P.H. Williams ◽  
J.N. Kriel
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Scalar Field ◽  
Lorentz Symmetry ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Dual Theory ◽  
Constructive Approach ◽  
Non Local ◽  
Exact Renormalization Group

We show that it is in principle possible to construct dualities between commutative and non-commutative theories in a systematic way. This construction exploits a generalization of the exact renormalization group equation (ERG). We apply this to the simple case of the Landau problem and then generalize it to the free and interacting non-canonical scalar field theory. This constructive approach offers the advantage of tracking the implementation of the Lorentz symmetry in the non-commutative dual theory. In principle, it allows for the construction of completely consistent non-commutative and non-local theories where the Lorentz symmetry and unitarity are still respected, but may be implemented in a highly non-trivial and non-local manner.

scholarly journals EXACT RENORMALIZATION GROUP EQUATION IN THE PRESENCE OF RESCALING ANOMALY II

2002 ◽  
Vol 17 (18) ◽  
pp. 1191-1205 ◽  
Author(s):  
STEFANO ARNONE ◽  
DARIO FRANCIA ◽  
KENSUKE YOSHIDA
Keyword(s):  
Renormalization Group ◽  
Exact Expression ◽  
Flow Equation ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Potential Term ◽  
Yang Mills ◽  
Text Model ◽  
The One ◽  
Exact Renormalization Group

Exact renormalization group techniques are applied to the mass deformed [Formula: see text] super-symmetric Yang–Mills theory, viewed as a regularized [Formula: see text] model. The solution of the flow equation, in case of dominance of the potential term, reproduces the one-loop (perturbatively exact) expression for the effective action of [Formula: see text] supersymmetric Yang–Mills theory, when the regularizing mass, M, reaches the value of the dynamical cutoff Λ. One speculates about the way in which further nonperturbative contributions (instanton effects) may be accounted for.

scholarly journals SUMMATION OF HIGHER ORDER EFFECTS USING THE RENORMALIZATION GROUP EQUATION

2005 ◽  
Vol 20 (05) ◽  
pp. 1065-1087 ◽  
Author(s):  
V. ELIAS ◽  
D. G. C. McKEON ◽  
T. N. SHERRY
Keyword(s):  
Renormalization Group ◽  
Method Of Characteristics ◽  
Thermal Field ◽  
Renormalization Group Equation ◽  
Higher Order ◽  
Massless Scalar ◽  
Order Effects ◽  
Group Equation ◽  
The Relationship ◽  
Higher Order Effects

The renormalization group (RG) is known to provide information about radiative corrections beyond the order in perturbation theory to which one has calculated explicitly. We first demonstrate the effect of the renormalization scheme used on these higher order effects determined by the RG. Particular attention is paid to the relationship between bare and renormalized quantities. Application of the method of characteristics to the RG equation to determine higher order effects is discussed and used to examine the free energy in thermal field theory, the relationship between the bare and renormalized coupling, and the effective potential in massless scalar electrodynamics.

scholarly journals RUNNING COUPLING CONSTANTS OF FERMIONS WITH MASSES IN QUANTUM ELECTRODYNAMICS AND QUANTUM CHROMODYNAMICS

2001 ◽  
Vol 16 (16) ◽  
pp. 2873-2894 ◽  
Author(s):  
GUANG-JIONG NI ◽  
GUO-HONG YANG ◽  
RONG-TANG FU ◽  
HAIBIN WANG
Keyword(s):  
Renormalization Group ◽  
Quantum Chromodynamics ◽  
Momentum Transfer ◽  
Quantum Electrodynamics ◽  
Renormalization Group Equation ◽  
Energy Scale ◽  
Coupling Constants ◽  
Group Equation ◽  
Running Coupling ◽  
Renormalization Method

Based on a simple but effective regularization-renormalization method (RRM), the running coupling constants (RCC) of fermions with masses in quantum electrodynamics (QED) and quantum chromodynamics (QCD) are calculated by renormalization group equation (RGE). Starting at Q=0 (Q being the momentum transfer), the RCC in QED increases with the increase of Q whereas the RCCs for different flavors of quarks with masses in QCD are different and they increase with the decrease of Q to reach a maximum at low Q for each flavor of quark and then decreases to zero at Q→0. Thus a constraint on the mass of light quarks, the hadronization energy scale of quark–antiquark pairs are derived.

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