# Performing integration over field variable

1. May 19, 2015

### aaaa202

I have this exercise, where I am to integrate out the fluctuations in the order parameter δρ, but I don't really know how to do this. The integral is over r and imaginary time. Should I try to complete the square, so the correlation term between δρ and Θ drops out? In that case which shift of variables should I make?

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2. May 24, 2015

### Greg Bernhardt

Yes, just complete the square. The shift of variable will simply be $\delta \rho \rightarrow \delta \rho - i \partial_r \theta /g$.