# Books on Covariant formulation of Electrodynamics

• Joker93
In summary, the conversation is about a student asking for book recommendations on the classical field theory of electromagnetism. Recommendations include Greiner's EM book, Landau&Lifshitz vol. II, and F. Scheck's Classical Field Theory.
Joker93
Hello!
I am an undergraduate currently enrolled in a course on theoretical physics. One big part of the course is on the classical field theory of electromagnetism(on its covariant formulation using Lagrangians mostly).
So, I would like to ask which are some good books on the subject.

@vanhees71 do you have some good recommendations that you use for your classes?

Dale said:
@vanhees71 do you have some good recommendations that you use for your classes?
Please note that I tried Greiner's EM book which contains a chapter on the covariant approach but we are using a lot more the field theory approach with Lagrangians and four vectors..

There is, of course, Landau&Lifshitz vol. II (Classical Field Theory), containing classical electrodynamics and general relativity. This volume concentrates on "microscopic electrodynamics". Electrodynamics in matter is treated in vol. VIII, which is also a masterpiece.

A even more modern approach, using the action principle for field theories, the idea of local gauge symmetries, etc. is vol. II of Scheck's theory-book series:

F. Scheck, Classical Field Theory, Springer-Verlag 2012

Joker93

## What is covariant formulation of Electrodynamics?

Covariant formulation of Electrodynamics is a mathematical framework that describes the behavior of electric and magnetic fields in a way that is independent of the observer's frame of reference. It incorporates the principles of special relativity and tensor calculus to provide a more fundamental and comprehensive understanding of electromagnetic phenomena.

## What are the main differences between the covariant and traditional formulations of Electrodynamics?

The traditional formulation of Electrodynamics is based on vector calculus and describes electric and magnetic fields in terms of three-dimensional vectors. In contrast, the covariant formulation uses tensor calculus and four-dimensional space-time to describe these fields. This allows for a more unified and consistent treatment of electromagnetic phenomena.

## What are some common applications of the covariant formulation of Electrodynamics?

The covariant formulation of Electrodynamics is widely used in modern physics, particularly in the fields of particle physics, general relativity, and cosmology. It is also essential in the development of quantum field theory, which is used to describe the behavior of subatomic particles.

## What are some key concepts and equations in the covariant formulation of Electrodynamics?

Some key concepts in the covariant formulation of Electrodynamics include the four-potential, the electromagnetic tensor, and the electromagnetic field equations. The main equations in this framework are Maxwell's equations, which describe the behavior of electric and magnetic fields, and the Lorentz force law, which describes the interaction between charged particles and these fields.

## Are there any limitations to the covariant formulation of Electrodynamics?

While the covariant formulation of Electrodynamics is a powerful and elegant framework, it does have some limitations. For example, it cannot fully describe the behavior of electromagnetic fields in highly curved space-time, such as near black holes. In these cases, a more comprehensive theory, such as quantum gravity, may be needed.

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