Coulomb Gauge and Gauge Transformation

In summary, the Coulomb gauge is a condition used in electromagnetism that sets the divergence of the vector potential to zero, eliminating the presence of Coulomb or longitudinal electric fields. It simplifies equations and has physical significance. A gauge transformation is a mathematical tool that can transform the vector potential and fields while maintaining physical results. The Coulomb gauge is a specific choice of gauge transformation that simplifies equations and allows for a better understanding of electric and magnetic fields. However, it is not always applicable and other gauge transformations may be used in certain situations.
  • #1
rodsika
279
2
I understand the conceptual meaning of gauge transformation which "can be broadly defined as any formal, systematic transformation of the potentials that leaves the fields invariant". I understand for example the U(1) and S(3) gauge symmetry in Gauge Theory. But what is this got to do with Coulomb gauge? Please use plain english in explaining and less on math because I'm not good in math but I just want to have general birds' eye view idea of coulomb gauge and how it is related to gauge transformation. Thanks.
 
Physics news on Phys.org
  • #2
Coulomb gauge is a specific way to fix the gauge
 

1. What is the Coulomb gauge in electromagnetism?

The Coulomb gauge is a mathematical condition used in electromagnetism that simplifies the equations describing the behavior of electric and magnetic fields by setting the divergence of the vector potential to zero. This effectively eliminates the presence of Coulomb or longitudinal electric fields.

2. What is the significance of the Coulomb gauge in electromagnetism?

The Coulomb gauge is important because it simplifies the equations of electromagnetism and makes them easier to solve. It also has physical significance, as it eliminates the presence of electric fields that do not contribute to the dynamics of the system.

3. What is a gauge transformation in electromagnetism?

A gauge transformation is a mathematical tool used to transform the vector potential and electric and magnetic fields to different values while keeping the physical results unchanged. It is a symmetry of the electromagnetic theory that allows us to choose different mathematical descriptions of the same physical system.

4. How does the Coulomb gauge relate to gauge transformations?

The Coulomb gauge is a specific choice of gauge transformation that sets the divergence of the vector potential to zero. This choice simplifies the equations of electromagnetism and allows for a more intuitive understanding of the behavior of electric and magnetic fields.

5. Can the Coulomb gauge always be applied in all situations?

No, the Coulomb gauge is not always applicable. It is a specific choice of gauge transformation that works well for certain systems, but there are situations where it may not be the best choice. In these cases, other gauge transformations may be used to simplify the equations of electromagnetism.

Similar threads

I Why is there a freedom to choose gauge in gauge transformation?
    • Electromagnetism
Replies
3
Views
843
I 4-Current vector potential transformation under Gauge fixing
    • Electromagnetism
Replies
5
Views
864
Lorentz and Gauge invariance of EM
    • Electromagnetism
Replies
4
Views
927
I Gauge and Phase Symmetries in Quantum Systems: Exploring the Confusion
    • Quantum Physics
Replies
6
Views
643
U(1) invariance of classical electromagnetism
    • Electromagnetism
Replies
29
Views
8K
A Gauge invariance confusions: symmetry vs redundancy, active vs passive
    • Quantum Physics
2
Replies
47
Views
4K
Conserved quantity for a particle in a homogeneous and static magnetic field
    • Electromagnetism
Replies
1
Views
981
What Is the Coulomb Gauge in Electromagnetic Theory?
    • Electromagnetism
Replies
3
Views
22K
A Orthogonality of variations in Faddev-Popov method for path integral
    • Quantum Physics
Replies
1
Views
628
Gauge Choice and Consistency with EOMs
    • Electromagnetism
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top