Samalkhaiat's challenge #001

  • #1
samalkhaiat
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Heh, heh, you should write a "Theoretical Physics Challenge" thread, similar to the "Math Challenges". :oldbiggrin:
Heh heh, unfortunately I can’t do that. However, many of my posts in here do (sometimes) contain exercises. I will try to make it a habit in the future. :smile:

Here is one relevant for relativity forum:
Use the definition [tex]T^{\mu\nu} = \frac{1}{\sqrt{-g}} \frac{\delta (\sqrt{-g}\mathcal{L})}{\delta g_{\mu\nu}} ,[/tex] to show that [tex]T^{\mu\nu} = V^{\mu}V^{\nu} (\rho - p) - g^{\mu\nu}p ,[/tex] is derivable from the Lagrangian [tex]\mathcal{L} = 2 \sigma (x) \left(1 + \pi (\sigma) \right) ,[/tex] where [itex]\sigma (x)[/itex] is the density of an isotropic fluid in some space-time region, and [itex]\pi (\sigma)[/itex] is the potential energy per unit density [itex]\sigma[/itex], i.e., the elastic potential of the fluid.

I think the solution is in Pauli's lectures on QFT
Are these in English?
or also in Bogoliubov&Shirkov.
I learnt QED from that book. In my opinion, it is the best book ever written on QED. I still use it whenever I get stuck on something.
 
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  • #2
strangerep
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However, many of my posts in here do (sometimes) contain exercises. I will try to make it a habit in the future. :smile:

Here is one relevant for relativity forum: [...]
I've asked the moderators to move this exercise into its own "challenge" thread. :cool:
 
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