1
$\begingroup$

I want resources for studying in detail the connection between the mathematical structures of physical theories and said physical theories.

For example, i know what a Hilbert space or a principal bundle is from a mathematical point of view and i know we use them in physics but i don't have any detail as how and where we use them.

This question arose from watching prof. Frederic Schuller's lectures on the geometrical anatomy of physical theory and lots of read-throughs in wikipedia. After all that i realised i knew about mathematical structure and about physics but not about how we use that mathematical structure in physics.

For example i know in QED we have a principal bundle with yang-mills field $ A_\mu $ and yang mills field strength $ F_{\mu\nu} $ which act as the electromagnetic 4-potential and Faraday tensor respectively but i don't know anything else about said bundle or the connection or how is this structure defined and i feel lost. I want a "tour" on the full anatomy of physical theories like QFT and general relativity. Does any such resource exist? Where can i find it if possible for free?

Improve this question
$\endgroup$
4
  • 1
    $\begingroup$ Perhaps The Road to Reality by Roger Penrose? Landau and Lifshitz? $\endgroup$
    – mmesser314
    Commented Feb 29 at 0:18
  • $\begingroup$ You probably won't find it for free. $\endgroup$
    – Albertus Magnus
    Commented Feb 29 at 0:19
  • $\begingroup$ Penrose definitely. L&L is a lift. Also Bernard Schutz "Geometrical Methods in Mathematical Physics" $\endgroup$
    – Cryo
    Commented Feb 29 at 4:36
  • $\begingroup$ Theodore Frankel "The Geometry of Physics" $\endgroup$
    – Cryo
    Commented Feb 29 at 4:37

0

Reset to default