Constructive Quantum Field Theory and Rigorous Statistical Mechanics via Operator Algebras and Probability Theory -- Guiding Principles and Research PerspectivesWe present a hierarchical viewpoint on the operator-algebraic formulation of quantum systems, in which C*-algebras are responsible for the universal and intrinsic description, whereas von…Yoshitsugu Sekine·Apr 7, 2026SaveLearn
A Two-HCIZ Gaussian Matrix Model for Non-intersecting Brownian BridgesWe construct a unitarily invariant Hermitian matrix ensemble whose fixed-time eigenvalue law coincides with the Karlin--McGregor law for non-intersecting Brownian bridges with arbitrary finite…Maksim Kosmakov·Apr 7, 2026SaveLearn
A note on measures whose diffraction is concentrated on a single sphereIs there a translation-bounded measure whose diffraction is spherically symmetric and concentrated on a single sphere? This note constructively answers this question of Strungaru in the affirmative.Michael Baake, Jan Mazáč, Emily R. Korfanty·Apr 7, 2026SaveLearn
Near-Tsirelson Bell-CHSH Violations in Quantum Field Theory via Carleman and Hankel OperatorsWe 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…David Dudal, Ken Vandermeersch·Apr 6, 2026SaveLearn
From BV-BFV Quantization to Reshetikhin-Turaev InvariantsWe propose a program for bridging the gap between the perturbative BV-BFV quantization of Chern-Simons theory and the non-perturbative Reshetikhin-Turaev (RT) invariants of 3-manifolds, passing…Nima Moshayedi·Apr 6, 2026SaveLearn
Ground states and droplet regimes of the extended Gross-Pitaevskii equation with Lee-Huang-Yang correctionWe study the ground states of the extended Gross--Pitaevskii equation with the Lee--Huang--Yang correction from both theoretical and numerical perspectives. Starting from the three-dimensional model,…Weijie Huang, Yang Liu, Xinran Ruan·Apr 6, 2026SaveLearn
Sharp upper bounds for the density of relativistic atoms: Noninteracting caseWe prove an optimal upper bound for the density of electrons of an infinite Bohr atom (no electron-electron interactions) described by the relativistic operators of Chandrasekhar and Dirac. We also…Rupert L. Frank, Konstantin Merz·Apr 5, 2026SaveLearn
Ergodic Schrodinger operators on the Bethe lattice and a modified Thouless formulaThe main result of this paper is a modified Thouless formula relating the density of states for ergodic Schrodinger operators on the Bethe lattice to the Lyapunov exponent. The modified Thouless…Peter D. Hislop, Christoph A. Marx·Apr 4, 2026SaveLearn
Variational formulation of a general dissipative fluid system with differential formsThis work is devoted to the study of dissipative fluid systems, through the lens of a geometric variational formulation. Building upon previous works extending Hamilton's principle to non-equilibrium…Bastien Manach-Pérennou, François Gay-Balmaz·Apr 4, 2026SaveLearn
Spatial Localization of Relativistic Quantum Systems: The Commutativity Requirement and the Locality Principle. Part I: A General AnalysisWe investigate whether commutativity is necessary to represent relativistic locality for localization observables of relativistic quantum systems in Minkowski spacetime. A well known no-go theorem by…Valter Moretti·Apr 4, 2026SaveLearn
Higher order derivative moments of CUE characteristic polynomials and the Riemann zeta functionWe use random matrix theory for the Circular Unitary Ensemble (CUE) to study moments of derivatives of the Riemann zeta function shifted a small distance from the critical line. The corresponding CUE…Alexander Grover, Francesco Mezzadri, Nick Simm·Apr 3, 2026SaveLearn
Cartan connections for an infinite family of integrable vorticesAn infinite family of integrable vortex equations is studied and related to the Cartan geometry of the underlying Riemann surfaces. This Cartan picture gives an interpretation of the vortex equations…Sven Bjarke Gudnason, Calum Ross·Apr 3, 2026SaveLearn
Dimensional consistency in fractional differential equations with non singular kernelsThe purpose of this article is to address the issues of dimensional consistency that arise in the process of replacing the ordinary time derivative operator by a fractional derivative operator in…Gabriel Gonzalez·Apr 2, 2026SaveLearn
Commutator Estimates for Low-Temperature Fermi GasesWe investigate the semiclassical regularity of thermal equilibria in the presence of a harmonic potential at low temperature; that is, we obtain the asymptotic behavior of the Schatten norms of…Jacky J. Chong, Laurent Lafleche, Jinyeop Lee et al.·Apr 2, 2026SaveLearn
A Rigorous Functional-Integral Construction of Toral Chern-Simons TheoryWe construct the functional integral of Abelian Chern-Simons theory with toral gauge group T= t/ U(1)n at level K, where K:× Z is an…Daniel Galviz·Apr 2, 2026SaveLearn
Functional relations in renormalization group methods for a class of ordinary differential equationsWe develop a renormalization group (RG)-based perturbation scheme for a class of ordinary differential equations, including first-order systems with semisimple or nilpotent linear parts, as well as…Atsuo Kuniba, Rurika Motohashi·Apr 2, 2026SaveLearn
Edge localization and Lifshitz tails for graphs with Ahlfors regular volume growthIn this work, we study the Anderson model on graphs with Ahlfors α-regular volume growth. We show that, under mild regularity assumptions of the random distribution, Lifshitz-tail type…Laura Shou, Wei Wang, Shiwen Zhang·Apr 2, 2026SaveLearn
A Note on the Resolvent Algebra and Functional Integral Approach to the Free Bose Einstein CondensationWe present a systematic description of the structure of Bose-Einstein condensation (BEC) in the free Bose gas from the viewpoint of the correspondence between the operator-algebraic formulation based…Yoshitsugu Sekine·Apr 1, 2026SaveLearn
Symmetries of (quasi)periodic materials: Superposability vs. IndistinguishabilityThis work is devoted to the study of the symmetries of (quasi)periodic architectured materials. For this purpose, the weaker symmetry criterion of indistinguishability is used. It relies on a…Markus Hubert, Christelle Combescure, Renald Brenner et al.·Apr 1, 2026SaveLearn
The Semiclassical Einstein-Klein-Gordon System: Asymptotic Analysis of Minkowski SpacetimeWe establish the linear instability of the semiclassical Einstein-Klein-Gordon system linearised about the Minkowski vacuum spacetime. The proof relies on formulating a forcing problem for both…Stefano Galanda, Paolo Meda, Simone Murro et al.·Apr 1, 2026SaveLearn
Toral Chern-Simons TQFT via Geometric Quantization in Real PolarizationWe construct toral Chern-Simons theory with gauge group T= t/ U(1)n from an even, integral, nondegenerate symmetric bilinear form K:× Z…Daniel Galviz·Apr 1, 2026SaveLearn
Dynkin diagrams, generalized Nahm sums and 2d CFTsA folklore conjecture states that the Nahm sum associated with a pair of Dynkin diagrams of type ADET is a modular function. In this paper, we extend this conjecture to Dynkin diagrams of type…Kaiwen Sun, Haowu Wang·Apr 1, 2026SaveLearn
Spectral sum rules on a d--sphereWe derive spectral sum rules for inverse powers of the eigenvalues of the Helmholtz equation on a d-sphere in the presence of an arbitrary density. By adopting a rigorous renormalization scheme, we…Paolo Amore·Apr 1, 2026SaveLearn
Local Rank-One Logarithmic Instability for the Mixed Hessian of the Dispersionless Toda τ-FunctionWe study a weighted renormalization of the mixed Hessian of the dispersionless Toda τ-function associated with polynomial conformal maps. The starting point is an explicit logarithmic-kernel…Oleg Alekseev·Mar 31, 2026SaveLearn
Symmetric Nonlinear Cellular Automata as Algebraic References for Rule~30A comparative algebraic framework for elementary cellular automata is developed, centered on the role of spatial symmetry. The primary object of study is Rule~22, the elementary cellular automaton…E. Chan-López, A. Martín-Ruiz·Mar 31, 2026SaveLearn