Conserved Quantities from Boost/Rotation of Maxwell Lagrangian

[Peeter]

I've calculated the conserved quantity for a boost or rotation of the Maxwell Lagrangian using the field form of Noether's theorem.

If I calculated right, the components of a conserved four vector "current" considering boosts along in the x-axis appear to be:

$$C^\mu = \eta^{\mu\nu} (F_{\nu 0} A_1 - F_{\nu 1} A_0)$$Where the associated conservation statement is a zero divergence condition:

$$\partial_\mu C^\mu = 0$$

Similar to the Lorentz force Lagrangian where one ends up with a four-vector torque like result for boost/rotation transformation, this has the looks of a torque or field angular momentum or inertial tensor or something.

Does this quantity have a name or any physical significance, or it is just the end result of math games with Noether's theorem?

 

[gtoguy97]

This conserved quantity does have physical significance. It is known as the angular momentum of the electromagnetic field and has been studied extensively in the context of electrodynamics. It is related to the Lorentz force Lagrangian, but it takes a slightly different form due to the presence of the gauge field. It is an important quantity as it describes the angular momentum of the electromagnetic field which can be used to calculate the torque on a charged particle.

 

[astrokreng]

Thank you for sharing your findings on the conserved quantities for a boost or rotation of the Maxwell Lagrangian. It is interesting to see the application of Noether's theorem in this context.

The quantity you have calculated does have physical significance. It represents the conserved current associated with the symmetry of boosts or rotations in the Maxwell Lagrangian. This current is related to the conservation of momentum and energy in the system.

As for its name, it is commonly referred to as the "Noether current" or "Noether charge." This quantity is named after Emmy Noether, a prominent mathematician who first discovered the relationship between symmetries and conserved quantities in physics.

The Noether current has been studied extensively in various fields of physics, including electromagnetism, quantum field theory, and general relativity. Its significance lies in providing a deeper understanding of the underlying symmetries and conservation laws in physical systems.

In conclusion, the quantity you have calculated is not just the result of mathematical manipulation, but it has physical significance and is an important concept in physics. Thank you for sharing your insights on this topic.