8 problems

Let $Z_N(\L,f)$ be the generating function for the scalar $\f^4$ theory with ultraviolet cutoff $N$, infrared region $\L$, and test function $f$. In dimension $d=4$ this is a renor…

Let $Z_N(\L,f)$ denote the ultraviolet-cutoff generating function of the scalar $\f^4$ theory in dimension $d=4$, with cutoff $N$, infrared region $\L$, and test function $f$. Beyo…

Let $k\in\mathbb{N}$, let $G\in\mathcal{S}\big((\mathbb{R}^{1,1})^k\big)$, and let $\alpha_1,\dots,\alpha_k$ be labels of solutions to the system a)–d). For each…

Triviality conjecture. For $d\geq 4$, the $\lambda\vert\boldsymbol{\phi}\vert^4$ theory of $\boldsymbol{\phi}$ is equivalent to a Gaussian (free) field theory.

Let $\nu_{\phi}$ be the non-Gaussian, translation-invariant, isotropic and scale-invariant BMS fixed-point measure on $S'(\mathbb{R}^3)$. The Osterwalder–Schrader positivity conjec…

The two-dimensional model is considered with coupling constant $\lambda$ of either sign. Wightman theory conjecture. The two-dimensional model can define a Wightman theory for any…

Let $d$ denote the space-time dimension, let $I(\f)$ be a fourth-order polynomial, and consider the naive discretization described above by Eq.equ{e2.4}. Naive-discretization conje…

The Sine-Gordon model is parametrized by the coupling … . The infinite-volume limit is the limit $\to\infty$, and exponential decrease of correlations means decay exponentially wit…