How Do You Calculate <A|0> in a Free Field Theory?

[hawcheese]

Homework Statement

Srednicki problem (8.8)

Under a free-field theory, calculate <A|0> , where |A> is the real sclar field's eigenket

Homework Equations

The Attempt at a Solution

I am trying to write <A|0> into path integral formulation, but it is hard.

 

[Avodyne]

As a function of momentum (rather than position), a free field is just a collection of harmonic oscillators. So for a given momentum mode, the ground state wave functional is just an appropriate gaussian. Then take a product over momentum modes, and convert the product of exponentials into the exponential of a sum (=integral).