The effect of renormalization in a finite massive theory

1995 ◽  
Vol 73 (9-10) ◽  
pp. 615-618
Author(s):  
D. G. C. McKeon
Keyword(s):  
Renormalization Group ◽  
Pole Mass ◽  
Coupling Constant ◽  
Loop Order ◽  
Effective Coupling ◽  
Yang Mills ◽  
Effective Coupling Constant ◽  
Group A ◽  
Massive Theory ◽  
Β Function

The fact that a theory is finite does not preclude the possibility of making finite renormalizations. With this in mind, we consider massive N = 4 super Yang–Mills theory, a model known to have a vanishing β function and to be finite at one-loop order when one uses the formulation using N = 1 superfields. The mass that appears in the Lagrangian is not a pole of the propagator when radiative effects are included; we fix the position of this pole and then discuss how the effective coupling constant in the theory depends on this pole mass. This procedure is akin to the original Gell-Mann–Low approach to the renormalization group. A one-loop calculation indicates that the effective coupling vanishes as the pole mass goes to zero and diverges for large values of the pole mass.

scholarly journals A MANIFESTLY GAUGE INVARIANT AND UNIVERSAL CALCULUS FORSU(N) YANG–MILLS

2006 ◽  
Vol 21 (23n24) ◽  
pp. 4627-4761 ◽  
Author(s):  
OLIVER J. ROSTEN
Keyword(s):  
Perturbation Theory ◽  
Renormalization Group ◽  
Explicit Dependence ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Group A ◽  
Β Function ◽  
Exact Renormalization Group

Within the framework of the Exact Renormalization Group, a manifestly gauge invariant calculus is constructed for SU (N) Yang–Mills. The methodology is comprehensively illustrated with a proof, to all orders in perturbation theory, that the β function has no explicit dependence on either the seed action or details of the covariantization of the cutoff. The cancellation of these nonuniversal contributions is done in an entirely diagrammatic fashion.

MODEL DEPENDENCE OF THE NON-MINIMAL SCALAR-GRAVITON EFFECTIVE COUPLING CONSTANT IN CURVED SPACE-TIME

1991 ◽  
Vol 06 (39) ◽  
pp. 3641-3646 ◽  
Author(s):  
T. MUTA ◽  
S. D. ODINTSOV
Keyword(s):  
Renormalization Group ◽  
Group Behavior ◽  
Space Time ◽  
Coupling Constant ◽  
Effective Coupling ◽  
Curved Space ◽  
Fermion Model ◽  
Conformally Invariant ◽  
Effective Coupling Constant ◽  
Model Dependence

We investigate the renormalization group behavior of the non-minimal scalar-graviton effective coupling constant in asymptotically free theories (where scalars are elementary) and in a simple four-fermion model (where scalars are composite). We find that this behavior is model-dependent in asymptotically free theories and is asymptotically conformally invariant in the four-fermion model. We observe that the behavior may be altered in more complicated four-fermion models.

RENORMALIZATION GROUP EQUATIONS AND DECONFINEMENT IN FINITE TEMPERATURE QCD

1991 ◽  
Vol 06 (27) ◽  
pp. 2475-2482
Author(s):  
GAO SONG ◽  
JIARONG LI
Keyword(s):  
Renormalization Group ◽  
High Temperature ◽  
Gauge Field ◽  
Finite Temperature ◽  
Anomalous Dimension ◽  
Coupling Constant ◽  
Effective Coupling ◽  
Effective Coupling Constant ◽  
Renormalization Group Equations ◽  
Finite Temperature Qcd

Finite temperature renormalization group equations are employed to investigate the behavior of the effective coupling constant and anomalous dimension in SU c(3) gauge field at finite temperature. On the basis of this, the deconfinement of high temperature QCD is discussed.

scholarly journals The renormalization group equations revisited

2018 ◽  
Vol 33 (26) ◽  
pp. 1830024 ◽  
Author(s):  
Jean-François Mathiot
Keyword(s):  
Renormalization Group ◽  
Dimensional Regularization ◽  
Direct Consequence ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Coupling Constant ◽  
Loop Order ◽  
Subtraction Scheme ◽  
Minimal Subtraction Scheme ◽  
Renormalization Group Equations

Starting from a well-defined local Lagrangian, we analyze the renormalization group equations in terms of the two different arbitrary scales associated with the regularization procedure and with the physical renormalization of the bare parameters, respectively. We apply our formalism to the minimal subtraction scheme using dimensional regularization. We first argue that the relevant regularization scale in this case should be dimensionless. By relating bare and renormalized parameters to physical observables, we calculate the coefficients of the renormalization group equation up to two-loop order in the [Formula: see text] theory. We show that the usual assumption, considering the bare parameters to be independent of the regularization scale, is not a direct consequence of any physical argument. The coefficients that we find in our two-loop calculation are identical to the standard practice. We finally comment on the decoupling properties of the renormalized coupling constant.

scholarly journals Effective coupling constant of plasmons

2019 ◽  
Vol 100 (5) ◽  
Author(s):  
Margaret E. Carrington ◽  
Stanisław Mrówczyński
Keyword(s):  
Coupling Constant ◽  
Effective Coupling ◽  
Effective Coupling Constant

Critical phenomena: Corrections to scaling behaviour

2021 ◽  
pp. 421-435
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Small Deviation ◽  
Critical Dimension ◽  
Coupling Constant ◽  
Effective Coupling ◽  
Corrections To Scaling ◽  
Upper Critical Dimension ◽  
Four Dimensions ◽  
Effective Coupling Constant ◽  
Scaling Behaviour ◽  
Leading Term

In preceding chapters, while deriving the scaling behaviour of correlation functions, we have always kept only the leading term in the critical region. We examine now the different corrections to the leading behaviour. For instance, when we have solved the renormalizaton group (RG) equations, so far, we have neglected the small deviation of the effective coupling constant from its fixed-point value. Moreover, to establish RG equations, we have neglected corrections subleading by powers of the cut-off, and effects of other couplings of higher canonical dimensions. Subleading terms related to the value of the effective coupling constant which give the leading corrections, at least near four dimensions, can easily be derived from the solutions of the renormalization group (RG) equations and are discussed first. The situations below and at four dimensions (the upper-critical dimension) have to be examined separately. The second type of corrections involves additional considerations and is examined in the second part of the chapter. The last section is devoted to one physics application, provided by systems with strong dipolar forces, which have 3 as upper-critical dimension.

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