Asymptotic freedom and the infrared problem: A novel solution to the renormalization-group equations

1983 ◽  
Vol 27 (6) ◽  
pp. 1402-1405 ◽  
Author(s):  
Geoffrey B. West
Keyword(s):  
Renormalization Group ◽  
Asymptotic Freedom ◽  
Renormalization Group Equations ◽  
Infrared Problem

scholarly journals PHASE TRANSITION IN GAUGE THEORIES, MONOPOLES AND THE MULTIPLE POINT PRINCIPLE

2005 ◽  
Vol 20 (26) ◽  
pp. 5911-5988 ◽  
Author(s):  
C. R. DAS ◽  
L. V. LAPERASHVILI
Keyword(s):  
Renormalization Group ◽  
Phase Transitions ◽  
Gauge Theories ◽  
Magnetic Charge ◽  
Coupling Constants ◽  
Asymptotic Freedom ◽  
Multiple Point ◽  
Group Model ◽  
Loop Approximation ◽  
Renormalization Group Equations

This review is devoted to the Multiple Point Principle (MPP), according to which several vacuum states with the same energy density exist in Nature. The MPP is implemented to the Standard Model (SM), Family replicated gauge group model (FRGGM) and phase transitions in gauge theories with/without monopoles. Using renormalization group equations for the SM, the effective potential in the two-loop approximation is investigated, and the existence of its postulated second minimum at the fundamental scale is confirmed. Phase transitions in the lattice gauge theories are reviewed. The lattice results for critical coupling constants are compared with those of the Higgs monopole model, in which the lattice artifact monopoles are replaced by the point-like Higgs scalar particles with magnetic charge. Considering our (3+1)-dimensional space–time as, in some way, discrete or imagining it as a lattice with a parameter a = λP, where λP is the Planck length, we have investigated the additional contributions of monopoles to the β-functions of renormalization group equations for running fine structure constants αi(μ) (i = 1, 2, 3 correspond to the U (1), SU(2) and SU(3) gauge groups of the SM) in the FRGGM extended beyond the SM at high energies. It is shown that monopoles have N fam times smaller magnetic charge in the FRGGM than in the SM (N fam is a number of families in the FRGGM). We have estimated also the enlargement of a number of fermions in the FRGGM leading to the suppression of the asymptotic freedom in the non-Abelian theory. We have reviewed that, in contrast to the case of the Anti-grand-unified-theory (AGUT), there exists a possibility of unification of all gauge interactions (including gravity) near the Planck scale due to monopoles. The possibility of the [SU(5)]3 or [SO(10)]3 unification at the GUT-scale ~1018 GeV is briefly considered.

scholarly journals Renormalization group equations of Higgs-R2 inflation

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Yohei Ema ◽  
Kyohei Mukaida ◽  
Jorinde van de Vis
Keyword(s):  
Renormalization Group ◽  
Standard Model ◽  
Planck Scale ◽  
Energy Scale ◽  
Einstein Frame ◽  
Ricci Scalar ◽  
Minimal Coupling ◽  
Renormalization Group Equations ◽  
The Standard Model

Abstract We derive one- and two-loop renormalization group equations (RGEs) of Higgs-R2 inflation. This model has a non-minimal coupling between the Higgs and the Ricci scalar and a Ricci scalar squared term on top of the standard model. The RGEs derived in this paper are valid as long as the energy scale of interest (in the Einstein frame) is below the Planck scale. We also discuss implications to the inflationary predictions and the electroweak vacuum metastability.

Renormalization group equations in lattice gauge theories

1978 ◽  
Vol 136 (2) ◽  
pp. 277-300 ◽  
Author(s):  
Tetsuo Matsui
Keyword(s):  
Renormalization Group ◽  
Gauge Theories ◽  
Lattice Gauge ◽  
Renormalization Group Equations ◽  
Lattice Gauge Theories

Prescription-independent renormalization group equations

1985 ◽  
Vol 44 (1) ◽  
pp. 61-63 ◽  
Author(s):  
F. Miglietta
Keyword(s):  
Renormalization Group ◽  
Renormalization Group Equations

Non-linear solutions of the renormalization group equations in the large-n limit

1977 ◽  
Vol 10 (7) ◽  
pp. 1175-1186 ◽  
Author(s):  
M Zannetti ◽  
C Di Castro
Keyword(s):  
Renormalization Group ◽  
Large N ◽  
Renormalization Group Equations ◽  
Non Linear

Infra-red behaviour of QED with Weinberg's and 't Hooft's renormalization group equations

1979 ◽  
Vol 25 (15) ◽  
pp. 467-472
Author(s):  
K. Kanaya
Keyword(s):  
Renormalization Group ◽  
Renormalization Group Equations ◽  
Infra Red

Asymptotic Freedom and the Renormalization Group

2018 ◽  
pp. 19-32
Author(s):  
A.M. Polyakov
Keyword(s):  
Renormalization Group ◽  
Asymptotic Freedom

Renormalization group equations of Briot-Bouquet type

1985 ◽  
Vol 28 (4) ◽  
pp. 555-558
Author(s):  
M. Visinescu
Keyword(s):  
Renormalization Group ◽  
Renormalization Group Equations
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