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Let $\mathscr{S}=\mathscr{S}(\mathbb{R}^d)$ be the space of real-valued Schwartz functions with its usual Frechet topology, and let $\mathscr{S}'=\mathscr{S}'(\mathbb{R}^d)$ be the space of real-value …

Coming a bit late to the party, but since there is no answer, let me offer one. Yes there is a program to make progress towards the YM problem, although with no guarantee of success in the end. The me …

The telescopic argument you mentioned is incorrect. If you carefully look at Rivasseau's notations, you will see that the first term $C^{0}(p)$ in the sum $$ \sum_{j=0}^{\rho}C^{j}(p) $$ is defined as …

Luckily for you, there is an online seminar where you can get a panorama of what is currently going on in the area of mathematical QFT. It is the webinar "Analysis, Quantum Fields, and Probability". T …

Not exactly an answer but too long for a comment. This is a very good question. You are right that the only nontrivial thing to check here is Osterwalder-Schrader positivity. The only proof I know is …

Just repeating my answer of the crosspost: https://math.stackexchange.com/questions/4198282/a-condition-for-the-vacuum-generating-functional According to the article (first paragraph of Sec. 4) the lo …

Although it might seem futile, given how far most of the activity on AdS/CFT is from rigorous mathematics, I think this a good question, provided one is happy, for now, with (very) baby versions of th …

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 …

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 …

The axioms don't tell you what theory you constructed. For that you need to go beyond the construction of correlation functions of the elementary field $\phi$ (the basic chapter on renormalization in …

Essentially, what is asked is the continuation of my previous MO answer Reformulation - Construction of thermodynamic limit for GFF and the solution of the exercise I mentioned at the end of that answ …

Focusing on exterior powers here is a distraction. The main problem already appears when considering the tensor algebra $T(E)=\oplus_{n\ge 0}E^{\otimes n}$. Once the issue is understood for the tensor …

For $x\in\mathbb{Z}^d$ I will denote by $\bar{x}$ the corresponding equivalence class in the discrete finite torus $\Lambda_{L}=\mathbb{Z}^d/L\mathbb{Z}^d$. I will view a field $\phi\in\mathbb{R}^{\La …

The source of the confusion is not saying explicitly what are the sets and $\sigma$-algebras the measures are supposed to be on. For example, a sentence like ''By Kolmogorov's Extension Theorem, there …

Good question! Before going further in your investigations on rigorous nonperturbative implementations of the renormalization group (RG) philosophy used for the construction of QFTs in the continuum, …