- #1
giant_bog
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I'm having problems with the equations leading up to eqn 2.45 on page 25. The hamiltonian has a [itex](\nabla\phi)^2 + m^2 \phi^2[/itex] term in the [itex]\phi(x)[/itex] commutator and in the [itex]\pi(x)[/itex] commutator it's [itex]\phi(-\nabla^2 + m^2) \phi[/itex].
I'm aware of a vector calculus identity that makes [itex](\nabla\phi)^2 = 1/2 (\nabla^2[\phi^2]) - \phi \nabla^2 \phi[/itex].
That's almost what we have here, but the [itex]\frac{1}{2}(\nabla^2[\phi^2])[/itex] term is missing in the [itex]\pi(x)[/itex] commutator.
Did anybody see where it went?
I'm aware of a vector calculus identity that makes [itex](\nabla\phi)^2 = 1/2 (\nabla^2[\phi^2]) - \phi \nabla^2 \phi[/itex].
That's almost what we have here, but the [itex]\frac{1}{2}(\nabla^2[\phi^2])[/itex] term is missing in the [itex]\pi(x)[/itex] commutator.
Did anybody see where it went?