Help With a Proof

1. Sep 14, 2004

Norman

I am unsure if this is the proper forum for this, since it is not actually homework... but here goes anyway.

I am trying to Prove Peskin and Schroeder equation 2.33

$$P=-\int d^3 x \pi (x) \nabla \phi (x) = \int \frac{d^3 x}{(2 \pi)^3} p a^{\dagger}_p a_p$$

so far what I have done:
written the fields as the momentum space quantities, done the integral over the spatial coordinates to give me the delta function and integrated over the p' variables to give me this:

The last step forces p'=-p

$$\int \frac{d^3}{(2 \pi)^3} \frac{p}{2} (a^{\dagger}_{-p} a_{-p} + a^{\dagger}_{-p} a^{\dagger}_p - a_p a_{-p} - a_p a^{\dagger}_p )$$

I don't see how these operators cancel out to give :
$$() = 2a^{\dagger}_p a_p$$

Any help would be greatly appreciated... even just a hint would be very helpfull.
Thanks

Last edited: Sep 17, 2004
2. Sep 14, 2004

Norman

Why isn't the latex coming up?

3. Sep 14, 2004

Tide

LaTeX seems to be broken - hope they get it fixed soon!

4. Sep 17, 2004

Norman

Now that LaTeX works...

Anyone able to lend a hand?