arXiv subjects

Ken Vandermeersch

Publications and source records attributed to Ken Vandermeersch.

4 recordsLinked to original sources

arXiv2026

Nilpotent groups with Dehn function $n^2 \log n$

We exhibit 2-step Carnot groups with Dehn function $n^2 \log n$, sharpening Wenger's superquadratic lower bound for these groups. Some of these groups admit lattices, yielding finitely generated nilpotent groups with Dehn function $n^2 \log n$. This gives the first exact computation of a Dehn function which does not grow like $n^\alpha$ for any $\alpha \geq 1$ among nilpotent groups and, more generally, among finitely presented solvable groups with subexponential Dehn function.

math.GR↗

arXiv2026

Near-Tsirelson Bell-CHSH Violations in Quantum Field Theory via Carleman and Hankel Operators

We study Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) violations in the vacuum state of free spinor fields in $(1+1)$-dimensional Minkowski spacetime. We construct explicit smooth compactly supported test functions with spacelike separated supports whose Bell-CHSH correlators converge to Tsirelson's bound $2\sqrt2$. In the massless case, after passage to the time-zero slice and a natural symmetry reduction, the problem reduces to the quadratic form of the Carleman operator on $L^2([0,\infty))$. Near-maximal Bell violation is then governed by the spectral edge $π$, and explicit near-extremizers are obtained from compactly supported cutoffs of the generalized eigenfunction $x^{-1/2}$. This also explains the appearance of the constant $π$ in earlier wavelet-based formulations. In the massive case, the same reduction leads to a Hankel operator with kernel $mK_1(m(x+y))$, where $K_1$ denotes the modified Bessel function of the second kind of order $1$, and exponentially damped variants of the massless test functions again yield Bell-CHSH values converging to $2\sqrt2$. Therefore, we establish a direct link between Bell-CHSH violations for free $(1+1)$-dimensional spinor fields and the spectral theory of Carleman and Hankel operators on the half-line.

math-ph↗

arXiv2026

Further Evidence for Near-Tsirelson Bell-CHSH Violations in Quantum Field Theory via Haar Wavelets

This paper investigates a recent construction using bumpified Haar wavelets to demonstrate explicit violations of the Bell-Clauser-Horne-Shimony-Holt inequality within the vacuum state in quantum field theory. The construction was tested for massless spinor fields in $(1+1)$-dimensional Minkowski spacetime and is claimed to achieve violations arbitrarily close to an upper bound known as Tsirelson's bound. We show that this claim can be reduced to a mathematical conjecture involving the maximal eigenvalue of a sequence of symmetric matrices composed of integrals of Haar wavelet products. More precisely, the asymptotic eigenvalue of this sequence should approach $π$. We present a formal argument using a subclass of wavelets, allowing us to reach $3.11052$. Although a complete proof remains elusive, we present further compelling numerical evidence to support it.

math-ph↗

arXiv2026

Automorphisms and monomorphisms of direct products of virtually solvable minimax groups

This paper studies automorphisms and monomorphisms of direct products $\Gamma=\Gamma_1\times\cdots\times\Gamma_r$ of finitely generated virtually solvable minimax groups, a class containing all virtually polycyclic groups. Under an indecomposability assumption on the $\mathbb Q$-algebraic hulls, we prove that every monomorphism of $\Gamma$ factorizes uniquely as $\varphi=\theta\cdot\zeta$, where $\theta$ sends each factor into a permuted factor with $\mathbb Q$-isomorphic hull and $\zeta$ is central and off-diagonal. Conversely, every such pair defines a monomorphism of $\Gamma$, and $\varphi$ is an automorphism if and only if $\theta$ is. This indecomposability assumption is sharp: we show it cannot be weakened to direct indecomposability of the factors. The proof proceeds in three steps: first by establishing the corresponding central mixing property for finite-dimensional Lie algebras and algebraic Lie algebras, then for connected linear algebraic groups, and finally by transferring these results to minimax groups via $\mathbb Q$-algebraic hulls. This extends the previously known nilpotent case both from automorphisms to monomorphisms and from finitely generated torsion-free nilpotent groups to the broader class of finitely generated virtually solvable minimax groups. As applications, we characterize co-Hopfian direct products and derive formulas for Reidemeister numbers and Reidemeister spectra.

math.GR↗