[ 1 post ] 
 Possible Error on p.489? 
Author Message

Joined: 12 Jul 2010, 07:44
Posts: 154
Post Possible Error on p.489?
At the top of the page, Penrose writes:

Quote:
The field equations then arise from the assertion that the quantity S is stationary with respect to variations of all the variables (so it gives the analogue of a geodesic; see Fig. 20.3), which means that the variational derivative of \mathcal{L} with respect to all the constituent fields and their derivatives has to vanish. This condition is written

\delta S = 0.


I'm thinking that he should have written S instead of \mathcal{L} in the above; i.e. that the variational derivative of S with respect to all the constituent fields and their derivatives has to vanish.

Of course, what Penrose wrote implies this (i.e. if the derivatives of \mathcal{L} vanish everywhere on D, then so do the derivatives of S). But if this were true, there'd be no Langrange equations! (Or rather, the Lagrange equations would degnerate to 0=0). That's because the Lagrange equations are composed of just such derivatives!


...or have I misinterpreted something?


04 Aug 2012, 12:38
   [ 1 post ]