The Electromagnetic Field

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
Electromagnetic Field ◽  
Gauge Invariance ◽  
Maxwell’S Equations ◽  
Green's Functions ◽  
Maxwell's Equations ◽  
Green’S Functions ◽  
Invariance Properties

The electromagnetic field. A brief review of Maxwell’s equations with a discussion of their invariance properties, both relativistic and gauge invariance. The formalism of Green’s functions is developed, including some physical applications.

scholarly journals Origin of Gauge Theories in Electrodynamics

2021 ◽  
Author(s):  
Jay Solanki
Keyword(s):  
Field Theory ◽  
Electromagnetic Field ◽  
Gauge Theory ◽  
Gauge Invariance ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Gauge Theories ◽  
Degree Of Freedom ◽  
Potential Formulation ◽  
Electromagnetic Field Theory

<div>The potential formulation has significant advantages over field formulation in solving complicated problems in electromagnetic field theory. One essential part of electromagnetic field theory's potential formulation is gauge invariance and gauge theories because it provides an extra degree of freedom. By using this extra degree of freedom, we can solve complicated electromagnetic problems quickly. Thus, it is necessary to include a systematic explanation of gauge theories in teaching electromagnetic theory. However, textbooks usually formulate gauge theories by using Maxwell's equations of electromagnetism, by using vector calculus identities. However, this method of formulation of gauge theories does not give a clear idea about the origin of gauge theories and gauge invariance in electromagnetism. Here the author formulates gauge theories from wave equations of the electric and magnetic fields instead of directly using Maxwell's equations. This method generalizes all gauge theories like Lorenz gauge theory, Coulomb gauge theory, Etc. Gauge theory, because of the way the author derives it, gives a distinct idea about the mathematical origin of the gauge theories and gauge invariance in electromagnetic field theory. Thus, the author reviews the origin of gauge theories in electromagnetic field theory and develops a distinct and effective method to introduce gauge theory in the teaching of electromagnetic field theory that can provide better understanding of the topic to undergraduate students.</div><div><br></div>

scholarly journals Origin of Gauge Theories in Electrodynamics

2021 ◽  
Author(s):  
Jay Solanki
Keyword(s):  
Field Theory ◽  
Electromagnetic Field ◽  
Gauge Theory ◽  
Gauge Invariance ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Gauge Theories ◽  
Degree Of Freedom ◽  
Potential Formulation ◽  
Electromagnetic Field Theory

<div>The potential formulation has significant advantages over field formulation in solving complicated problems in electromagnetic field theory. One essential part of electromagnetic field theory's potential formulation is gauge invariance and gauge theories because it provides an extra degree of freedom. By using this extra degree of freedom, we can solve complicated electromagnetic problems quickly. Thus, it is necessary to include a systematic explanation of gauge theories in teaching electromagnetic theory. However, textbooks usually formulate gauge theories by using Maxwell's equations of electromagnetism, by using vector calculus identities. However, this method of formulation of gauge theories does not give a clear idea about the origin of gauge theories and gauge invariance in electromagnetism. Here the author formulates gauge theories from wave equations of the electric and magnetic fields instead of directly using Maxwell's equations. This method generalizes all gauge theories like Lorenz gauge theory, Coulomb gauge theory, Etc. Gauge theory, because of the way the author derives it, gives a distinct idea about the mathematical origin of the gauge theories and gauge invariance in electromagnetic field theory. Thus, the author reviews the origin of gauge theories in electromagnetic field theory and develops a distinct and effective method to introduce gauge theory in the teaching of electromagnetic field theory that can provide better understanding of the topic to undergraduate students.</div><div><br></div>

Electromagnetic field behavior of 3D Maxwell's equations for chiral media

2019 ◽  
Vol 379 ◽  
pp. 118-131 ◽  
Author(s):  
Tsung-Ming Huang ◽  
Tiexiang Li ◽  
Ruey-Lin Chern ◽  
Wen-Wei Lin
Keyword(s):  
Electromagnetic Field ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Chiral Media ◽  
Field Behavior

scholarly journals Some remarks on the charging capacitor problem

2018 ◽  
Vol 7 (2) ◽  
pp. 10-12
Author(s):  
C. J. Papachristou
Keyword(s):  
Electromagnetic Field ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Displacement Current ◽  
Standard Textbook ◽  
Maxwell Displacement Current

The charging capacitor is the standard textbook and classroom example for explaining the concept of the so-called Maxwell displacement current. A certain aspect of the problem, however, is often overlooked. It concerns the conditions for satisfaction of the Faraday-Henry law inside the capacitor. Expressions for the electromagnetic field are derived that properly satisfy all four of Maxwell’s equations in that region.

scholarly journals On How QCD Gauge Invariance Gets Realized in the Context of Effective Locality

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
H. M. Fried ◽  
T. Grandou ◽  
R. Hofmann
Keyword(s):  
Gauge Invariance ◽  
Degrees Of Freedom ◽  
Green's Functions ◽  
Green’S Functions ◽  
The Way

The fermionic Green’s functions of QCD exhibit an unexpected property of effective locality, which appears to be exact, involving no approximation. This property is nonperturbative, resulting from a full integration of the elementary gluonic degrees of freedom of QCD. Recalling, correcting, and extending the derivations of effective locality, focus is put on the way nonabelian gauge invariance gets realized in the fermionic nonperturbative regime of QCD.

XI.—Electromagnetic Phenomena in a Uniform Gravitational Field

1932 ◽  
Vol 51 ◽  
pp. 71-79 ◽  
Author(s):  
D. Meksyn
Keyword(s):  
Electromagnetic Field ◽  
Gravitational Field ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Suitable Choice ◽  
Fundamental Tensor

In two recent papers Professor E. T. Whittaker has solved the electromagnetic equations for the case of a uniform gravitational field. The fundamental tensor associated with such a field makes the Riemannian tensor vanish, since such a field can be transformed away by a suitable choice of coordinates. This property enables us to find the electromagnetic field in a uniform gravitational field without solving Maxwell's equations, but by a mere transformation of co-ordinates.

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