# Complicated commutator QFT

1. Apr 8, 2009

### waht

1. The problem statement, all variables and given/known data

When calculating this commutator,

$$[ \pi(x), \int d^3x' { \frac{1}{2} \pi^2(x') + \frac{1}{2} \phi(x')(-\nabla^2 + m^2) \phi(x') }]$$

I almost get the right answer, but not sure if this is valid, or if there is an identity

3. The attempt at a solution

when I get to this point

$$\int d^3x' \pi(x) \phi(x')( -\nabla^2 \phi(x')) - \phi(x') (-\nabla^2 \phi(x'))\pi(x)$$

I need to take out $$-\nabla^2 \phi(x')$$ to form

$$(-\nabla^2 \phi(x')) [\pi(x), \phi(x')]$$

that way the rest would follow and give me the correct answer which is

$$-i(-\nabla^2 + m^2)\phi(x'))$$

Last edited: Apr 8, 2009