15 problems

The state space of a quantum system is a Hilbert space, and bound electron states in a molecule may have an intrinsic two-valuedness. Different electrons, and later other fermions,…

Gibbsianness conjecture. The fermion random point field $\mu^{(J)}$ is a Gibbs measure for the specification in Proposition 1.

Let $m$ be the mass of the $\varsigma$ particle and let $M_\mathrm{Ch}$ and $R_\mathrm{Ch}$ denote the corresponding critical Chandrasekhar mass and radius of a remanent dark-matte…

Crossover-scale conjecture. The crossover range is universally estimated by

Alpha-determinantal point-process conjecture. The limiting point processes in these cases can be described by $alpha$-determinantal point processes.

Let $b^*(k)$ and $b(k)$ be the particle-hole creation and annihilation operators, and let $\Omega$ denote the vacuum vector. The operators $b^*(k)$ commute pairwise, and the vacuum…

Consider the semilocal Abelian case $N_c=1$, $N_f=\lambda$, with the vortex theory in the setting described in the source. Fermionic duality conjecture. The vortex theory is dual t…

For the harmonic oscillator $V(x)=\frac{1}{2}x^2$, let $x^+=\sqrt{\beta N}$ be the right edge and let $w_N=\frac{\sqrt{\beta}}{2}N^{-1/6}$ be the width of the edge region. For…

Let ${\rm Var}\,\mathcal N_{[a,b]}$ denote the variance of the number of fermions in an interval $[a,b]$, and let higher cumulants mean the cumulants of order greater than two. Mic…

BC-term conjecture. The $BC$ term can have an effect analogous to the terms $\frac{k}{4\pi}AdA$ with odd integer $k$ in $(2+1)$ dimensions and $BB$ in $(3+1)$ dimensions: a bosonic…

Let $K$ be a knot, and let $D^{2}\times K$ be its knotted solid-torus neighborhood. A hyperbolic knot complement is a 3-manifold … that admits a homogeneous hyperbolic metric. Hype…

The paper studies higher-spin massive fermionic fields in $2+1$ dimensions. For spin $\frac{3}{2}$, the construction suggests that the nonlinear nature of the fields is compatible…

The paper constructs massive fermionic fields in $2+1$ dimensions and, for spin $\frac{3}{2}$, finds an underlying structure associated with the nonlinear behaviour of the boost op…

Let $N$ spinless fermions in $\operatorname{\mathbb{R}}^3$ have normalized wave function $\psi$ and one-particle density $\rho$. Their kinetic energy is … The sharp semiclassical L…

In a theory obtained by deforming a conventional CPT-even local free fermion theory with a non-local factor, consider CPT breaking in the free fermion sector, including effects ari…