# Tag Info

Accepted

### Formal mathematical definition of renormalization group flow

The renormalization group (RG) as a geometric flow (like the Ricci flow) is a very special case of the RG, namely, the one corresponding to the nonlinear sigma-model (NLSM) in two dimensions with ...

### Formal mathematical definition of renormalization group flow

Classical field theories (Lagrangian variational principles) sometimes come in families. The families may be finite dimensional, or also infinite dimensional. One could even take the family to consist ...
• 21.2k

### Simple example of renormalization

The simplest and earliest example I know regarding the renormalization group idea is the following. Suppose we want to study some feature $\mathcal{Z}(\vec{V})$ of some object $\vec{V}$ which is in a ...

### Renormalization in physics vs. dynamical systems

The renormalization approach to dynamical systems pioneered by Chen, Goldenfeld and Oono [1] applies the Gell-Mann and Low renormalization group from quantum physics [2] to extract the global behavior ...
• 181k

### Non-perturbative Renormalization in the sense of Polchinski's equation. Do we have a mathematical formulation?

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, ...
Accepted

Accepted

### How can one recover/obtain information from the renormalization group procedure?

The limiting function $V^\ast$ is such that any further convolutions of $e^{-V^\ast}$ with $\mu$ return $e^{-V^\ast}$, so $Z^\ast(\phi)=e^{-V^\ast(\phi)}$. To obtain critical properties, you need the ...
• 181k
Accepted

### Cluster expansion, Mayer expansion and perturbative renormalization group

I think there is a misunderstanding here on what is the expansion parameter. Perturbative renormalization expands in a power series of the interaction strength (the coupling parameter $\lambda$); this ...
• 181k
1 vote
Accepted

### The ultraviolet limit as a limiting case of the renormalization group flow?

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 ...
1 vote
Accepted

### Singular Radon probabilities on $[0,1]^d$. Is conditioning on $x_i = \alpha$ well-defined?

$\newcommand{\B}{\mathcal B}$ First here, $[0,1]^d$ is a Polish space (i.e., a separable complete metric space). So, $[0,1]^d$ is a Radon space, and hence any (Borel) probability measure is Radon. So, ...
• 120k
1 vote

### Why does the type-A subdivision algebra look like the Rota-Baxter algebra axiom?

This is too long for a comment. The reason for my question in comments was as follows. In some cases (Gerstenhaber algebras, Poisson algebras, etc.) an operad describing a certain algebraic structure ...
• 16.8k

Only top scored, non community-wiki answers of a minimum length are eligible