Integrating by parts Maxwell Lagrangian

In summary, The conversation discusses the free EM action integral and how it can be rewritten. The individual is seeking help on how to go from the first line to the second, specifically how to handle the indices of the gauge fields. They mention integrating by parts and throwing out surface terms, but are unsure of the next steps. They also ask if anyone has seen a text where this is derived and express confusion on how to proceed from their current equation.
  • #1
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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
 

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  • #2
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?
 

1. What is the purpose of integrating by parts in the Maxwell Lagrangian?

The purpose of integrating by parts in the Maxwell Lagrangian is to simplify the equations of motion for electromagnetic fields by breaking them down into more manageable parts. This allows for easier analysis and calculation of physical properties.

2. How does integrating by parts affect the Maxwell Lagrangian equations?

Integrating by parts in the Maxwell Lagrangian affects the equations by reducing them to a set of simpler equations that are easier to solve. It also allows for the identification and isolation of specific terms, making it easier to analyze the behavior of electromagnetic fields.

3. What is the process for integrating by parts in the Maxwell Lagrangian?

The process for integrating by parts in the Maxwell Lagrangian involves breaking down the equation into two parts and then integrating one part while differentiating the other. This is repeated until the equation is simplified to a more manageable form.

4. What are the benefits of using integrating by parts in the Maxwell Lagrangian?

There are several benefits to using integrating by parts in the Maxwell Lagrangian. It simplifies the equations of motion, allows for easier analysis and calculation of physical properties, and also allows for the identification and isolation of specific terms for further study.

5. Are there any limitations to using integrating by parts in the Maxwell Lagrangian?

While integrating by parts in the Maxwell Lagrangian is a useful tool, it may not always be applicable or appropriate for every situation. It also requires a good understanding of the underlying principles and equations, and may not always result in a completely simplified form.

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