7 problems

Let ${\Lambda_0}$ be fixed and let $T\geq 0$. For the convergent part of the theory, denote by…

Four-dimensional Yang–Mills measure-properties conjecture. The classic Hamiltonian system can be quantized so that $\mu^g$ exists, $S^g$ satisfies the Osterwalder–Schrader axioms (…

Nonperturbative constructive QFT conjecture. It is conjectured that eventually one could well-define an interacting quantum field theory model in a nonperturbative manner, in a con…

Let $C^{j\to}_{1,1}(\xi)$ be the scale-$j$ contribution to the two-point function, with $\xi=(\tau,\boldsymbol{x})$, and let $\mu$ be the parameter appearing in the scale bounds. T…

A scalar quantum field theory in dimension $4$ is said to have nontrivial Schwinger functions when its Schwinger functions do not coincide with those of the free field. Triviality…

Glimm–Jaffe spectrum condition conjecture. The spectrum condition should also hold for Hamiltonians defined on the spatial circle:

The model is defined by the action … where $\Theta$ is the deformation matrix defining the associative product $\star$, and $Z$, $\mu^2$, $\lambda$, and $\Omega$ are the relevant o…