I would like to understand the derivation of (1.3),
 
$$ \int_{C_{\rm{per}}([0,L])} \phi(x_1) \phi(x_2) d\mu_G(\phi) = \text{tr } e^{-x_1 H} \phi e^{(x_2 - x_1)H} / \text{tr }  e^{-LH} $$

 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.