Norman
- 895
- 4
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
[tex]P=-\int d^3 x \pi (x) \nabla \phi (x) = \int \frac{d^3 x}{(2 \pi)^3} p a^{\dagger}_p a_p[/tex]
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
[tex]\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 )[/tex]
I don't see how these operators cancel out to give :
[tex]() = 2a^{\dagger}_p a_p[/tex]
Any help would be greatly appreciated... even just a hint would be very helpfull.
Thanks
I am trying to Prove Peskin and Schroeder equation 2.33
[tex]P=-\int d^3 x \pi (x) \nabla \phi (x) = \int \frac{d^3 x}{(2 \pi)^3} p a^{\dagger}_p a_p[/tex]
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
[tex]\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 )[/tex]
I don't see how these operators cancel out to give :
[tex]() = 2a^{\dagger}_p a_p[/tex]
Any help would be greatly appreciated... even just a hint would be very helpfull.
Thanks
Last edited: