28 problems

Infrared-finiteness conjecture. With the right choice of the numerical part of the current, there are no infrared divergences in the formalism of L-functionals if, in perturbation…

Runaway-solution conjecture. A particular kind of runaway solution may exist in relativistic spin-1/2 quantum electrodynamics.

Fix an integer $N$. For a periodic box of size $L$, let $E_L^N(\varphi)$ be the Hartree–Fock minimum in the charge sector with trace $N$, let $E_L(0)$ be the corresponding vacuum e…

Let $H(P_{3})$ be the fiber Hamiltonian at longitudinal momentum $P_{3}$ acting on the Hilbert space $\mathcal H$, and remove the infrared regularization from the quantized electro…

Fix a radius $R_0>0$. The localization theorem provides balls $B_1,\dots,B_n$ in $\mathbb{R}^3$, each of radius $R_0$, and a normalized vector $\Psi$ in the physical Hilbert space…

Optimality conjecture. The choice of trial wave function used in the proof is optimal, in the sense that Equation holds as equality apart from errors of order…

Sharpness conjecture. Apart from errors of order $o(\alpha)$, Equation should hold with equality.

Let $\mathcal{L}^{(l)(\mathrm{SD})}(\kappa)$ denote the loop-order $l$ weak-field effective Lagrangian in a constant self-dual background, with fine-structure constant $\alpha$, ma…

Let $\alpha$ denote the physical fine structure constant, and consider loopwise summation of quantum electrodynamics with an eigenvalue for $\alpha$, uniformly across all fermion s…

The dyon quantum electrodynamics (dQED) model is an alternative formulation of quantum electrodynamics with magnetic monopoles, based on the Cabibbo–Ferrari and Salam approach. Its…

More precise conjecture. To get rid of infrared divergences in the inclusive cross section of some process, one should choose the numerical part of the current to coincide with the…

Let $\psi^{(1)}$ denote the first-order correction to the free incoming Dirac field, and let the corresponding first- and higher-order corrections to the electromagnetic current be…

Let $e_q$ denote the physical ground state energy of the electron-positron Hartree–Fock model, obtained by maximizing the model's ground state energy over all allowed one-particle…

Let $\mathcal{E}_V$ be the Maxwell–Schrödinger energy functional for a spin-$\frac12$ electron, and let $g>0$ be the coupling constant. Two minimizers are identified when they diff…

Let $c$ be a real smearing function on the sphere with total weight $1$, and define … Let $c_0(e)=\frac{1}{4\pi}$ be the constant smearing, for which $\langle c_0,c_0\rangle=1$. Gl…

Let $a_n^{(l)}$ denote the perturbative expansion coefficient at loop order $l$, and let $n$ index the weak-field expansion. The leading weak-electric corrections to the imaginary…

Ritus' conjecture. The weak-field instanton expansion of its non-perturbative imaginary part has the form

Let $\eta$ be a profile, let $\mathrm{v}$ be a four-velocity, let $C\in\{F^{\mu\nu},j^\mu\}$ be an observable field, and let $\Psi,\Psi'\in\mathcal{D}_2$. The BRST charge is denote…

Let $\phi(x,e)$ be the escort field and let $h(e)$ be a fixed function of the string direction with zero total integral. Define … The corresponding correlation functions are those…

Let $L^{\mathrm{s}}$ be the string-localized interaction Lagrangian, $L^{\mathrm{p}}$ the corresponding point-local interaction, $\psi_{gL^{\mathrm{s}}}$ the interacting Dirac fiel…

Let QFD$_3$ denote the theory with the smallest non-trivial value of $N_f^{(2)}$, equivalently the $U(1)_{-1/2}$ theory or QED$_3$ with $N_f=\frac{1}{2}$ when counting four-compone…

Strong resolvent convergence conjecture. In the sense of strong convergence of resolvents,

The model describes outgoing observables in a fixed forward lightcone, with charged particles whose asymptotic position variable is not available in the unmodified asymptotic frame…

Consider the dressed helium ion $\mathrm{He}^+$ at fixed total momentum, whose nucleus consists of two protons and is treated as a spin-$0$ particle. Kramers-degeneracy conjecture.…

Let $E_g(P)$ denote the ground-state energy of the hydrogen atom Hamiltonian in non-relativistic QED at coupling $g$ and fixed total momentum $P$. Simplicity conjecture. The eigenv…