scholarly journals Influence of exact Lorentz-violating mechanism on the critical exponents for massive q-deformed λϕ4 scalar field theory

2019 ◽  
Vol 28 (08) ◽  
pp. 1950105
Author(s):  
P. R. S. Carvalho ◽  
M. I. Sena-Junior
Keyword(s):  
Scalar Field ◽  
Critical Exponents ◽  
Field Theories ◽  
Quantum Corrections ◽  
Leading Order ◽  
Independent Field ◽  
Group Methods ◽  
Breaking Mechanism ◽  
Lorentz Symmetry Breaking ◽  
Renormalization Group Methods

We probe the influence of Lorentz-violating mechanism, treated exactly, on the radiative quantum corrections to critical exponents for massive [Formula: see text]-deformed O([Formula: see text]) [Formula: see text] scalar field theories. We attain that task by employing three distinct and independent field-theoretic renormalization group methods. Firstly, we compute the critical exponents up to the finite next-to-leading order for then generalizing the results for any loop level. We show that the [Formula: see text]-deformed critical exponents are insensible to the Lorentz symmetry breaking mechanism thus agreeing with the universality hypothesis.

scholarly journals Exact Lorentz-violating q-deformed O(N) universality class

2019 ◽  
Vol 28 (03) ◽  
pp. 1950050
Author(s):  
P. R. S. Carvalho ◽  
M. I. Sena-Junior
Keyword(s):  
Critical Exponents ◽  
Universality Class ◽  
Field Theories ◽  
Quantum Corrections ◽  
Leading Order ◽  
Loop Order ◽  
Independent Field ◽  
Group Methods ◽  
Renormalization Group Methods ◽  
Finite Loop

We examine the influence of exact Lorentz-violating symmetry mechanism on the radiative quantum corrections to the critical exponents for massless [Formula: see text]-deformed O([Formula: see text]) [Formula: see text] scalar field theories. For that, we employ three different and independent field-theoretic renormalization group methods for computing analytically the [Formula: see text]-deformed critical exponents up to next-to-leading order. Then, we generalize the former finite loop level results for any loop order. We show that the Lorentz-violating [Formula: see text]-deformed critical exponents, obtained through the three methods, turn out to be identical and furthermore the same as their Lorentz-invariant [Formula: see text]-deformed ones. We argue that this result is in accordance with the universality hypothesis.

scholarly journals NLO critical exponents of O(N) λ ϕ4 scalar field theories in curved spacetime

2019 ◽  
Vol 28 (01) ◽  
pp. 1950024
Author(s):  
H. A. S. Costa ◽  
P. R. S. Carvalho
Keyword(s):  
Scalar Field ◽  
Critical Exponents ◽  
Conformal Symmetry ◽  
Field Theories ◽  
Quantum Corrections ◽  
Leading Order ◽  
Loop Order ◽  
Curved Spacetime ◽  
Flat Spacetime

In this paper, we investigate analytically the conformal symmetry influence on the next-to-leading order radiative quantum corrections to critical exponents for massless O([Formula: see text]) [Formula: see text] scalar field theories in curved spacetime. We renormalize the theory by applying the Bogoliubov–Parasyuk–Hepp–Zimmermann (BPHZ) method. We find that the critical exponents are the same as that of flat spacetime, at least at the loop order considered. We argue that this result agrees perfectly with the universality hypothesis.

scholarly journals Unconventional minimal subtraction and Callan–Symanzik methods for Lorentz-violating scalar field theories at all loop orders

2018 ◽  
Vol 15 (05) ◽  
pp. 1850086 ◽  
Author(s):  
G. S. Silva ◽  
P. R. S. Carvalho
Keyword(s):  
Scalar Field ◽  
Critical Exponents ◽  
Field Theories ◽  
Quantum Corrections ◽  
Leading Order ◽  
Minimal Subtraction ◽  
Analytical Computation ◽  
Induction Process ◽  
Time In Literature ◽  
First Time

We present an explicit analytical computation of the quantum corrections, at next-to-leading order, to the critical exponents. We employ for that the Unconventional minimal subtraction, recently proposed, and the Callan–Symanzik methods to probe the universality hypothesis by comparing the outcomes for the critical exponents evaluated in both methods and the ones calculated previously in massless theories renormalized at different renormalization schemes. Furthermore, the consistency of the former method is investigated for the first time in literature, to our knowledge. At the end, we compute the critical exponents at any loop level by an induction process and furnish the physical interpretation of the results.

A class of inflaton potentials from RG analysis of scalar-gravity interaction

2014 ◽  
Vol 11 (02) ◽  
pp. 1460008
Author(s):  
Artur R. Pietrykowski
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Observational Data ◽  
Particle Physics ◽  
Field System ◽  
Group Methods ◽  
Renormalization Group Methods ◽  
Scalar Gravity ◽  
Inflationary Models ◽  
The Way

Inflationary models are characterized by the form of a potential which is arbitrary and usually parametrized so as to match the observational data. However, making use of the renormalization group methods to a gravity-scalar field system it is possible to find physically nontrivial potentials that might be relevant for cosmology and particle physics as well. I will pinpoint the way this class of potentials may be found as well as discuss their utility for inflationary models.

Simulation and Modeling of Turbulent Flows

1996 ◽  
Keyword(s):  
Numerical Simulation ◽  
Turbulent Flow ◽  
Turbulent Flows ◽  
Simulation And Modeling ◽  
Simulation Techniques ◽  
Rational Development ◽  
Group Methods ◽  
Turbulent Closure ◽  
The Subject ◽  
Renormalization Group Methods

This book provides students and researchers in fluid engineering with an up-to-date overview of turbulent flow research in the areas of simulation and modeling. A key element of the book is the systematic, rational development of turbulence closure models and related aspects of modern turbulent flow theory and prediction. Starting with a review of the spectral dynamics of homogenous and inhomogeneous turbulent flows, succeeding chapters deal with numerical simulation techniques, renormalization group methods and turbulent closure modeling. Each chapter is authored by recognized leaders in their respective fields, and each provides a thorough and cohesive treatment of the subject.

scholarly journals Quantum corrections to slow-roll inflation: scalar and tensor modes

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Jens O. Andersen ◽  
Magdalena Eriksson ◽  
Anders Tranberg
Keyword(s):  
Scalar Field ◽  
Quantum Corrections ◽  
Tree Level ◽  
Field Equations ◽  
Slow Roll ◽  
Scalar Field Equations ◽  
Slow Rolling ◽  
Different Sources ◽  
Suitable Potential ◽  
Quadratic Order

Abstract Inflation is often described through the dynamics of a scalar field, slow-rolling in a suitable potential. Ultimately, this inflaton must be identified with the expectation value of a quantum field, evolving in a quantum effective potential. The shape of this potential is determined by the underlying tree-level potential, dressed by quantum corrections from the scalar field itself and the metric perturbations. Following [1], we compute the effective scalar field equations and the corrected Friedmann equations to quadratic order in both scalar field, scalar metric and tensor perturbations. We identify the quantum corrections from different sources at leading order in slow-roll, and estimate their magnitude in benchmark models of inflation. We comment on the implications of non-minimal coupling to gravity in this context.

scholarly journals Renormalization group methods and the 2PI effective action

2015 ◽  
Vol 91 (2) ◽  
Author(s):  
M. E. Carrington ◽  
Wei-Jie Fu ◽  
D. Pickering ◽  
J. W. Pulver
Keyword(s):  
Renormalization Group ◽  
Effective Action ◽  
Group Methods ◽  
Renormalization Group Methods
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