Help: Mode Decomposition and Retarded Feilds and Green's functions

[zamoura]

Hello,

I studying General Relativity at University of Chicago and I am looking for information regarding "Fourier-Harmonic Mode Decomposition" or mode decomposition in general and "Retarded Greens Functions" and retarded fields in general.

Does anyone have advice about where is a good place to learn about these subjects? All this material is very new to me so and help would be very much appreciated.

Thanks,
Zamoura

 

[Peeter]

The book 'mathematics of classical and quantum physics' by Byron and Fuller (Dover) has a nice treatment of Green's functions, including retarded and advanced solutions of the wave equation. It may not be exactly what you are looking for, but may be a good starting place.

 

[Entropia]

Hi Zamoura,

Mode decomposition is a technique used to break down a complex system or function into simpler components or modes. It is commonly used in physics and engineering to analyze systems with multiple variables or components. In the context of General Relativity, mode decomposition is used to study the behavior of gravitational fields in terms of their different modes or frequencies.

Retarded fields and Green's functions are closely related concepts in electromagnetism and quantum field theory. Retarded fields are solutions to the wave equation that describe the behavior of electromagnetic fields at a particular point in space and time, taking into account the time delay due to the finite speed of light. Green's functions, on the other hand, are mathematical tools used to solve differential equations and are particularly useful in finding solutions for the electromagnetic fields in the presence of sources.

To learn more about these topics, I would recommend starting with some introductory textbooks on General Relativity and Electromagnetism. "Gravitation" by Misner, Thorne, and Wheeler is a classic text on General Relativity that covers mode decomposition in depth. For electromagnetism, "Introduction to Electrodynamics" by David Griffiths is a great resource that covers Green's functions and retarded fields.

You can also find online lectures and resources from universities such as MIT and Stanford that cover these topics in detail. Additionally, discussing these concepts with your professors and peers can also help deepen your understanding.

I hope this helps and good luck with your studies!