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There is also a new method which gets a hold of eigenvectors directly by an iterative diagonalization procedure rather than indirectly via expectations of products of resolvents. It is in the recent a …

One of the best books on statistical mechanics and its mathematical aspects is "Statistical Mechanics, A Short Treatise" by G. Gallavotti, Springer, 1999: Google Books link.

@Sarah: I have some reservations about how the question is framed since it already answers itself and makes QFT seems like a subject which is completely separate from mathematics with occasional and a …

I don't think Onsager's solution will help you in the presence of a magnetic field. In the low temperature regime there are rigorous expansions for pretty much all the quantities of interest. These go …

An excellent introduction for a mathematician without previous exposure to quantum field theory is the book by Gerald Folland: "Quantum field theory, a tourist guide for mathematicians", ISBN: 978-0-8 …

Modern constructive field theory is based on rigorous implementations of the renormalization group (RG) approach. To get an idea of what this is about see this short introductory paper. The RG is an i …

@HyyFly: It would be nice to elaborate a bit on your question and in particular give some motivation. What applications do you have in mind for possible generalizations of the Hubbard-Stratonovich tra …

Of course the physics literature is full of references on path integrals. One would not know where to start. Kleinert's books suggested by Alexander must be a good choice. On the rigorous side you mig …

There is a very nice treatment of this question in the textbook by Konrad Schmüdgen "Unbounded Self-adjoint Operators on Hilbert Space", see in particular Theorem 5.23 p. 103. While there is no probl …

I have the book right in front of me and from a quick glance at the relevant section it seems that GJ chose a somewhat non-standard presentation. I think the most commonly used approach is the one exp …

In statistical mechanics one is mostly interested in some fixed probability measure for some spin configurations on the infinite volume lattice $\mathbb{Z}^d$. The two main problems related to such a …

There has been many answers, from many points of view on QFT: canonical quantization, algebraic QFT, etc. Let me add another perspective using the Euclidean path integral quantization, as emphasized i …

Let me add to Daniel's list a couple links to some hopefully pedagogical notes I wrote for a course I taught a while ago. Notes on the cluster expansion for the polymer gas, a.k.a., the Mayer expans …

Only a small addendum to the excellent answer by Paul Garrett: A place where the Fourier transform is worked out explicitly (in 1d) is this preprint by Burnol. See in particular Page 13.

There is no space cutoff because it is $d(x,y)$ which depends on the two points. If you put a constant $c$ in your integral $\int_c^\infty d\tau$ then yes you would have introduced a spurrious cutoff …