scholarly journals Fermion and photon gap-equations in Minkowski space within the Nakanishi integral representation method

2021 ◽  
Vol 81 (1) ◽  
Author(s):  
Cédric Mezrag ◽  
Giovanni Salmè
Keyword(s):  
Integral Representation ◽  
Minkowski Space ◽  
Integral Equations ◽  
Vector Boson ◽  
Coupled System ◽  
The Self ◽  
Consistency Check ◽  
System Of Integral Equations ◽  
Perturbative Regime ◽  
Representation Method

AbstractThe approach based on the Nakanishi integral representation of n-leg transition amplitudes is extended to the treatment of the self-energies of a fermion and an (IR-regulated) vector boson, in order to pave the way for constructing a comprehensive application of the technique to both gap- and Bethe-Salpeter equations, in Minkowski space. The achieved result, namely a 6-channel coupled system of integral equations, eventually allows one to determine the three Källén–Lehman weights for fully dressing the propagators of fermion and photon. A first consistency check is also provided. The presented formal elaboration points to embed the characteristics of the non-perturbative regime at a more fundamental level. It yields a viable tool in Minkowski space for the phenomenological investigation of strongly interacting theories, within a QFT framework where the dynamical ingredients are made transparent and under control.

The Problem of Several Indentors Moving on a Viscoelastic Half-Plane

1995 ◽  
Vol 62 (2) ◽  
pp. 380-389 ◽  
Author(s):  
H. Z. Fan ◽  
G. A. C. Graham ◽  
J. M. Golden
Keyword(s):  
Steady State ◽  
Boundary Value Problem ◽  
Integral Equations ◽  
Half Plane ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Coupled System ◽  
Mixed Boundary Value Problem ◽  
System Of Integral Equations ◽  
Space And Time

The problem of several indentors moving on a viscoelastic half-plane is considered in the noninertial approximation. The solution of this mixed boundary value problem is formulated in terms of a coupled system of integral equations in space and time. These are solved numerically in the steady-state limit for the case of two indentors. The phenomena of hysteretic friction and interaction between the two indentors are explored.

scholarly journals Existence results for nonlinear coupled system of integral equations of Urysohn Volterra-Chandrasekhar mixed type

2020 ◽  
Vol 53 (1) ◽  
pp. 236-248
Author(s):  
Tamer Nabil
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Nuclear Physics ◽  
Mixed Type ◽  
Coupled System ◽  
Existence Of A Solution ◽  
System Of Integral Equations ◽  
Nonlinear Coupled System ◽  
Systems Of Integral Equations ◽  
Quadratic Integral

AbstractThe combined systems of integral equations have become of great importance in various fields of sciences such as electromagnetic and nuclear physics. New classes of the merged type of Urysohn Volterra-Chandrasekhar quadratic integral equations are proposed in this paper. This proposed system involves fractional Urysohn Volterra kernels and also Chandrasekhar kernels. The solvability of a coupled system of integral equations of Urysohn Volterra-Chandrasekhar mixed type is studied. To realize the existence of a solution of those mixed systems, we use the Perov’s fixed point combined with the Leray-Schauder fixed point approach in generalized Banach algebra spaces.

scholarly journals Solvability of an infinite system of integral equations on the real half-axis

2020 ◽  
Vol 10 (1) ◽  
pp. 202-216
Author(s):  
Józef Banaś ◽  
Weronika Woś
Keyword(s):  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Main Tool ◽  
Supremum Norm ◽  
Nonlinear Integral Equations ◽  
Measures Of Noncompactness ◽  
System Of Integral Equations ◽  
The Real ◽  
Half Axis

Abstract The aim of the paper is to investigate the solvability of an infinite system of nonlinear integral equations on the real half-axis. The considerations will be located in the space of function sequences which are bounded at every point of the half-axis. The main tool used in the investigations is the technique associated with measures of noncompactness in the space of functions defined, continuous and bounded on the real half-axis with values in the space l∞ consisting of real bounded sequences endowed with the standard supremum norm. The essential role in our considerations is played by the fact that we will use a measure of noncompactness constructed on the basis of a measure of noncompactness in the mentioned sequence space l∞. An example illustrating our result will be included.

Constant-Sign Lp Solutions for a System of Integral Equations

2004 ◽  
Vol 46 (3-4) ◽  
pp. 195-219 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Donal O’Regan ◽  
Patricia J. Y. Wong
Keyword(s):  
Integral Equations ◽  
Constant Sign ◽  
System Of Integral Equations ◽  
Lp Solutions

scholarly journals Fixed Point Results for the Family of Multivalued F-Contractive Mappings on Closed Ball in Complete Dislocated b-Metric Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 56 ◽  
Author(s):  
Qasim Mahmood ◽  
Abdullah Shoaib ◽  
Tahair Rasham ◽  
Muhammad Arshad
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Metric Spaces ◽  
Closed Ball ◽  
Multivalued Mappings ◽  
System Of Integral Equations ◽  
Contractive Mappings ◽  
The Family ◽  
Rational Type

The purpose of this paper is to find out fixed point results for the family of multivalued mappings fulfilling a generalized rational type F-contractive conditions on a closed ball in complete dislocated b-metric space. An application to the system of integral equations is presented to show the novelty of our results. Our results extend several comparable results in the existing literature.

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