Exact Nonperturbative Solution of a Nonlinear Fermion-Field Equation of Motion

1972 ◽  
Vol 6 (6) ◽  
pp. 1543-1553 ◽  
Author(s):  
E. van der Spuy
Keyword(s):  
Field Equation ◽  
Equation Of Motion ◽  
Fermion Field ◽  
Nonperturbative Solution

scholarly journals DILATON COUPLED QUINTESSENCE MODEL IN THE ω - ω′ PLANE

2007 ◽  
Vol 16 (07) ◽  
pp. 1109-1117 ◽  
Author(s):  
Z. G. HUANG ◽  
H. Q. LU ◽  
W. FANG
Keyword(s):  
Dark Energy ◽  
Field Equation ◽  
Scalar Field ◽  
Equation Of State ◽  
State Parameter ◽  
Equation Of Motion ◽  
Gravitational Theory ◽  
Scalar Field Equation ◽  
Equation Of State Parameter ◽  
Quintessence Model

In this paper, we regard the dilaton in Weyl-scaled induced gravitational theory as a coupled quintessence. Based on this consideration, we investigate the dilaton coupled quintessence (DCQ) model in the ω - ω′ plane, which is defined by the equation of state parameter for the dark energy and its derivative with respect to N (the logarithm of the scale factor a). We find the scalar field equation of motion in the ω - ω′ plane, and show mathematically the properties of attractor solutions which correspond to ωσ ~ -1, ωσ = 1. Finally, we find that our model is a tracking one which belongs to "freezing" type models classified in the ω - ω′ plane.

scholarly journals Electromagnetic field with induced massive term: Case with scalar field

Open Physics ◽  
2011 ◽  
Vol 9 (5) ◽  
Author(s):  
Yuri Rybakov ◽  
Georgi Shikin ◽  
Yuri Popov ◽  
Bijan Saha
Keyword(s):  
Electromagnetic Field ◽  
Field Equation ◽  
Scalar Field ◽  
Cosmological Model ◽  
Bianchi Type ◽  
Rest Mass ◽  
Additional Term ◽  
Equation Of Motion ◽  
Massless Scalar ◽  
Type I

AbstractWe consider an interacting system of massless scalar and electromagnetic fields, with the Lagrangian explicitly depending on the electromagnetic potentials, i.e., interaction with broken gauge invariance. The Lagrangian for interaction is chosen in such a way that the electromagnetic field equation acquires an additional term, which in some cases is proportional to the vector potential of the electromagnetic field. This equation can be interpreted as the equation of motion of photon with induced nonzero rest-mass. This system of interacting fields is considered within the scope of Bianchi type-I (BI) cosmological model. It is shown that, as a result of interaction the isotropization process of the expansion takes place.

The Einstein field equation

2021 ◽  
pp. 213-226
Author(s):  
Andrew M. Steane
Keyword(s):  
Field Theory ◽  
Field Equation ◽  
Einstein Field Equation ◽  
Equation Of Motion ◽  
Energy Conditions ◽  
Gravitational Fields ◽  
Electromagnetic Field Theory ◽  
Stationary Conditions ◽  
Energy And Momentum ◽  
Insight Into

Various aspects of the Einstein field equation are presented. First the field equation is obtained by arguing that it is the simplest equation that respects the fundamental geometric insight into gravity. Then we consider whether the equation is stable, and introduce the weak energy and dominant energy conditions. The connection between inertial motion and the distant universe (Mach’s principle) is discussed. The equation of motion of matter is obtained from the field equation, and a comparison made with electromagnetic field theory. The energy and momentum of gravitational fields in stationary conditions is discussed, and the Komar energy obtained.

scholarly journals Thermal, trapped and chromo-natural inflation in light of the swampland criteria and the trans-Planckian censorship conjecture

2021 ◽  
Vol 81 (5) ◽  
Author(s):  
Arjun Berera ◽  
Robert Brandenberger ◽  
Vahid Kamali ◽  
Rudnei O. Ramos
Keyword(s):  
Field Equation ◽  
Scalar Field ◽  
High Energy ◽  
Equation Of Motion ◽  
Energy Scale ◽  
The Other ◽  
Grand Unification ◽  
Scalar Field Equation ◽  
Low Energies ◽  
High Energy Scale

AbstractWe consider thermal, trapped and chromo-natural inflation in light of the swampland criteria and the Trans-Planckian Censorship Conjecture (TCC). Since thermal inflation occurs at energies low compared to those of Grand Unification, it is consistent with the TCC, and it is also consistent with the refined swampland conditions. Trapped and chromo-natural inflation are candidates for primordial (high energy scale) inflation. Since in both of these scenarios there are effective damping terms in the scalar field equation of motion, the models can easily be consistent with the swampland criteria. The TCC, on the other hand, constrains these scenarios to only take place at low energies.

Particle motion with air resistance

2012 ◽  
Vol 8 (1) ◽  
pp. 1-15
Author(s):  
Gy. Sitkei
Keyword(s):  
Basic Equation ◽  
Initial Conditions ◽  
Equation Of Motion ◽  
Terminal Velocity ◽  
Dimensionless Form ◽  
Wood Industry ◽  
Acceptable Error ◽  
General Validity ◽  
Practical Applications ◽  
Air Resistance

Motion of particles with air resistance (e.g. horizontal and inclined throwing) plays an important role in many technological processes in agriculture, wood industry and several other fields. Although, the basic equation of motion of this problem is well known, however, the solutions for practical applications are not sufficient. In this article working diagrams were developed for quick estimation of the throwing distance and the terminal velocity. Approximate solution procedures are presented in closed form with acceptable error. The working diagrams provide with arbitrary initial conditions in dimensionless form of general validity.

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