Integrating by parts Maxwell Lagrangian

Click For Summary
SUMMARY

The discussion focuses on integrating by parts within the context of the free electromagnetic (EM) action integral in the Maxwell Lagrangian. The user seeks clarity on the transition from the initial expression to a rewritten form, emphasizing the handling of gauge field indices during integration. Key points include the elimination of surface terms and the correct treatment of upper and lower indices for the gauge fields. The user expresses a need for resources or texts that derive this integration process.

PREREQUISITES
  • Understanding of the Maxwell Lagrangian and electromagnetic action integrals.
  • Familiarity with integration by parts in the context of field theory.
  • Knowledge of gauge field theory and index notation.
  • Basic concepts of variational principles in physics.
NEXT STEPS
  • Study the derivation of the free electromagnetic action integral in classical field theory.
  • Learn about integration by parts specifically applied to field theory contexts.
  • Research gauge field index manipulation techniques in theoretical physics.
  • Explore variational principles and their applications in deriving equations of motion.
USEFUL FOR

The discussion is beneficial for theoretical physicists, graduate students in physics, and researchers focusing on classical field theory and gauge theories.

Lapidus
Messages
344
Reaction score
12
I attached a file that shows the free EM action integral and how it can be rewritten. I would like to know how to go from the first line to the second. I have to integrate by parts somehow, and I know surface terms get thrown out, but I do not know how the indices of the gauge fields should be handled.

thanks for any help
 

Attachments

Physics news on Phys.org
Has then perhaps anybody seen a text were it is derived?

I got -A∂∂A + A∂∂A, and both terms upper indices for A∂ and lower indices for ∂A. But what now? How to get to the last line?
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 9 ·
Replies
9
Views
9K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 13 ·
Replies
13
Views
2K