Gauge Transformation: Coulomb to Lorentz

Thread starter catlike
Start date Apr 28, 2012
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Gauge Gauge transformation Transformation

In summary, A gauge transformation is a mathematical operation used in physics to change the description of a physical system without altering its physical properties. It is often used in electromagnetism to simplify calculations and express physical quantities in a more convenient form. In Coulomb gauge, the electric potential is chosen to be zero, while in Lorentz gauge, the divergence of the vector potential is set to be zero. This results in different mathematical descriptions of the electromagnetic field, but they are physically equivalent. A gauge transformation does not change the physical properties of the electromagnetic field, but it can change its mathematical description. This means that the values of physical quantities, such as electric and magnetic fields, will remain the same, but their mathematical expressions may be different. The

Apr 28, 2012

catlike

Find a gauge transformation which maps the Coulomb gauge to the Lorentz gauge?

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Apr 29, 2012

clamtrox

You should start by looking up how the gauges are defined

Apr 29, 2012

Dale

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Insights Author

You may get a better response by posting this in the homework sub-forum and showing your attempt so far.

What is a gauge transformation?

A gauge transformation is a mathematical operation used in physics to change the description of a physical system without altering its physical properties. It is often used in electromagnetism to simplify calculations and express physical quantities in a more convenient form.

What is the difference between Coulomb gauge and Lorentz gauge?

In Coulomb gauge, the electric potential is chosen to be zero, while in Lorentz gauge, the divergence of the vector potential is set to be zero. This results in different mathematical descriptions of the electromagnetic field, but they are physically equivalent.

How does a gauge transformation affect the electromagnetic field?

A gauge transformation does not change the physical properties of the electromagnetic field, but it can change its mathematical description. This means that the values of physical quantities, such as electric and magnetic fields, will remain the same, but their mathematical expressions may be different.

Why is the Coulomb gauge more convenient for some calculations?

The Coulomb gauge is often used in situations where there are no time-varying electric fields. In this gauge, the equations for the electromagnetic field become simpler and easier to solve, making it more convenient for certain calculations.

What is the physical significance of a gauge transformation?

A gauge transformation does not have a physical significance, as it does not affect the physical properties of a system. It is simply a mathematical tool used to simplify calculations and express physical quantities in a more convenient form.