Reddit mentions of Introduction to Many-Body Physics

Does anyone have any experience with the new book, Introduction to Many-Body Physics by Piers Coleman?

I'm not sure what you mean by a "field study". If you mean experiments, then yes, there are likely hundreds or thousands, as this is well-established theory that predicts numerous results in condensed matter physics; e.g. electronic properties of metals, superconductivity, superfluidity, etc.

This topic can be found in any of the standard texts on many-body physics, a subject also often referred to as condensed-matter quantum field theory. My favorites are "AGD" (i.e. the guys who invented this technique), Mahan, and Coleman (which is the most pedagogical of the three).

If you're looking for something to Google, you might want to try "finite temperature field theory" and "Matsubara formalism".

I'm not sure what your level is, but this is pretty technical stuff; I literally never heard of these concepts (other than randomly hearing the phrase "imaginary time") until taking a graduate course on many-body theory. I honestly don't know of any popular books that discuss finite temperature QFT in detail (not that I'm particularly well-versed in the popular literature, but it doesn't seem like the kind of thing that usually makes its way into the usual "multiverse/wormhole/strings/black holes" books). If you want to know more in detail, but don't know what a time evolution operator is, you'll need to learn basic nonrelativistic quantum mechanics; R. Shankar's book is a good way to learn about that, though Griffiths is a bit more accessible.