https://doi.org/10.1140/epjc/s10052-026-15559-6
Regular Article - Theoretical Physics
Further evidence for near-Tsirelson Bell–CHSH violations in quantum field theory via Haar wavelets
1
Department of Physics, KU Leuven Campus Kortrijk-Kulak, Etienne Sabbelaan 53, 8500, Kortrijk, Belgium
2
Department of Mathematics, KU Leuven Campus Kortrijk-Kulak, Etienne Sabbelaan 53, 8500, Kortrijk, Belgium
a
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Received:
9
January
2026
Accepted:
10
March
2026
Published online:
6
April
2026
Abstract
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 
-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 may 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 
. We present a formal argument using a subclass of wavelets, allowing to reach 3.11052. Although a complete proof remains elusive, we present further compelling numerical evidence to support it.
© The Author(s) 2026
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