scholarly journals The weak-gravity bound and the need for spin in asymptotically safe matter-gravity models

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Gustavo P. de Brito ◽  
Astrid Eichhorn ◽  
Rafael Robson Lino dos Santos
Keyword(s):  
Fixed Point ◽  
Higher Order ◽  
Gravity Models ◽  
Asymptotic Safety ◽  
Critical Strength ◽  
Scalar Gravity ◽  
Weak Gravity

Abstract We discover a weak-gravity bound in scalar-gravity systems in the asymptotic-safety paradigm. The weak-gravity bound arises in these systems under the approximations we make, when gravitational fluctuations exceed a critical strength. Beyond this critical strength, gravitational fluctuations can generate complex fixed-point values in higher-order scalar interactions. Asymptotic safety can thus only be realized at sufficiently weak gravitational interactions. We find that within truncations of the matter-gravity dynamics, the fixed point lies beyond the critical strength, unless spinning matter, i.e., fermions and vectors, is also included in the model.

scholarly journals Effective universality in quantum gravity

2018 ◽  
Vol 5 (4) ◽  
Author(s):  
Astrid Eichhorn ◽  
Peter Labus ◽  
Jan M. Pawlowski ◽  
Manuel Reichert
Keyword(s):  
Fixed Point ◽  
Quantum Gravity ◽  
Qualitative Agreement ◽  
Quantitative Agreement ◽  
Quantum Level ◽  
Asymptotic Safety ◽  
Gravity System ◽  
Scalar Gravity

We investigate the asymptotic safety scenario for a scalar-gravity system. This system contains two avatars of the dynamical Newton coupling, a gravitational self-coupling and a scalar-graviton coupling. We uncover an effective universality for the dynamical Newton coupling on the quantum level: its momentum-dependent avatars are in remarkable quantitative agreement in the scaling regime of the UV fixed point. For the background Newton coupling, this effective universality is not present, but qualitative agreement remains.

scholarly journals ASYMPTOTIC SAFETY IN HIGHER-DERIVATIVE GRAVITY

2009 ◽  
Vol 24 (28) ◽  
pp. 2233-2241 ◽  
Author(s):  
DARIO BENEDETTI ◽  
PEDRO F. MACHADO ◽  
FRANK SAUERESSIG
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Renormalization Group Flow ◽  
Functional Renormalization Group ◽  
Asymptotic Safety ◽  
Higher Derivative ◽  
Gravity Theories ◽  
Group Flow ◽  
Nonperturbative Renormalization

We study the nonperturbative renormalization group flow of higher-derivative gravity employing functional renormalization group techniques. The nonperturbative contributions to the β-functions shift the known perturbative ultraviolet fixed point into a nontrivial fixed point with three UV-attractive and one UV-repulsive eigendirections, consistent with the asymptotic safety conjecture of gravity. The implication of this transition on the unitarity problem, typically haunting higher-derivative gravity theories, is discussed.

scholarly journals A Study of Nonlinear Boundary Value Problem

2021 ◽  
Author(s):  
Noureddine Bouteraa ◽  
Habib Djourdem
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Iterative Method ◽  
Boundary Value Problem ◽  
Higher Order ◽  
Nonlinear Boundary Value Problem ◽  
Point Boundary ◽  
Error Estimations ◽  
Fractional Differential

In this chapter, firstly we apply the iterative method to establish the existence of the positive solution for a type of nonlinear singular higher-order fractional differential equation with fractional multi-point boundary conditions. Explicit iterative sequences are given to approximate the solutions and the error estimations are also given. Secondly, we cover the multi-valued case of our problem. We investigate it for nonconvex compact valued multifunctions via a fixed point theorem for multivalued maps due to Covitz and Nadler. Two illustrative examples are presented at the end to illustrate the validity of our results.

scholarly journals Equivalence of two fixed-point semantics for definitional higher-order logic programs

2017 ◽  
Vol 668 ◽  
pp. 27-42 ◽  
Author(s):  
Angelos Charalambidis ◽  
Panos Rondogiannis ◽  
Ioanna Symeonidou
Keyword(s):  
Fixed Point ◽  
Higher Order ◽  
Order Logic ◽  
Logic Programs ◽  
Higher Order Logic ◽  
Fixed Point Semantics

Relating renormalizability of D-dimensional higher-order electromagnetic and gravitational models to the classical potential at the origin

2017 ◽  
Vol 32 (08) ◽  
pp. 1750048 ◽  
Author(s):  
Antonio Accioly ◽  
Gilson Correia ◽  
Gustavo P. de Brito ◽  
José de Almeida ◽  
Wallace Herdy
Keyword(s):  
Fourth Order ◽  
Massive Gravity ◽  
Higher Order ◽  
Sixth Order ◽  
Gravity Models ◽  
Local Models ◽  
Order Model ◽  
Functional Generator ◽  
Classical Potential ◽  
Real Poles

Simple prescriptions for computing the D-dimensional classical potential related to electromagnetic and gravitational models, based on the functional generator, are built out. These recipes are employed afterward as a support for probing the premise that renormalizable higher-order systems have a finite classical potential at the origin. It is also shown that the opposite of the conjecture above is not true. In other words, if a higher-order model is renormalizable, it is necessarily endowed with a finite classical potential at the origin, but the reverse of this statement is untrue. The systems used to check the conjecture were D-dimensional fourth-order Lee–Wick electrodynamics, and the D-dimensional fourth- and sixth-order gravity models. A special attention is devoted to New Massive Gravity (NMG) since it was the analysis of this model that inspired our surmise. In particular, we made use of our premise to resolve trivially the issue of the renormalizability of NMG, which was initially considered to be renormalizable, but it was shown some years later to be non-renormalizable. We remark that our analysis is restricted to local models in which the propagator has simple and real poles.

scholarly journals An EKF-Based Fixed-Point Iterative Filter for Nonlinear Systems

Sensors ◽  
2019 ◽  
Vol 19 (8) ◽  
pp. 1893
Author(s):  
Feng ◽  
Feng ◽  
Wen
Keyword(s):  
Fixed Point ◽  
Kalman Filter ◽  
Nonlinear Systems ◽  
Iterative Method ◽  
Taylor Series ◽  
Nonlinear Filtering ◽  
Higher Order ◽  
Point Function ◽  
State Estimate ◽  
Linearized System

In this paper, a fixed-point iterative filter developed from the classical extended Kalman filter (EKF) was proposed for general nonlinear systems. As a nonlinear filter developed from EKF, the state estimate was obtained by applying the Kalman filter to the linearized system by discarding the higher-order Taylor series items of the original nonlinear system. In order to reduce the influence of the discarded higher-order Taylor series items and improve the filtering accuracy of the obtained state estimate of the steady-state EKF, a fixed-point function was solved though a nested iterative method, which resulted in a fixed-point iterative filter. The convergence of the fixed-point function is also discussed, which provided the existing conditions of the fixed-point iterative filter. Then, Steffensen’s iterative method is presented to accelerate the solution of the fixed-point function. The final simulation is provided to illustrate the feasibility and the effectiveness of the proposed nonlinear filtering method.

scholarly journals Higher Order of Convergence with Multivalued Contraction Mappings

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Jia-Bao Liu ◽  
Asma Rashid Butt ◽  
Shahzad Nadeem ◽  
Shahbaz Ali ◽  
Muhammad Shoaib
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Order Of Convergence ◽  
Higher Order ◽  
Gauge Function ◽  
Multivalued Mappings ◽  
Contraction Mappings ◽  
Multivalued Contraction ◽  
Integral Inclusion

In this paper, we establish some theorems of fixed point on multivalued mappings satisfying contraction mapping by using gauge function. Furthermore, we use Q - and R -order of convergence. Our main results extend many previous existing results in the literature. Consequently, to substantiate the validity of proposed method, we give its application in integral inclusion.

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