The lecture notes appeared in the second volume of "Quantum Fields and Strings, a course for mathematicians". I would like to understand the derivation of (1.3), the 2-point correlation function:

$$ \int_{C_{\rm{per}}([0,L])} \phi(x_1) \phi(x_2) d\mu_G(\phi) = \text{tr } e^{-x_1 H} \phi e^{(x_2 - x_1)H} / \text{tr } e^{-LH} $$

which is listed as a problem, under the heading of Feynman kac's formula. Specifically I would like to know how exactly $\mu_G$ is defined and how it relates to Wiener measure.

On a more practical note, I would like to know what's a good source (if not here) for obtaining solutions to these sporadic exercises in high level lecture notes. Since time is limited, those of us who do not want to specialize in an area, but only want to get a taste of a subject, but do not want to sacrifice rigor, might find this kind of information very useful.