Mathematical Physics
In this paper, we study the Connes spectral distance between states on the fuzzy torus. We construct a Dirac operator by commutators and anticommutators. Based on this Dirac operator, we construct a spectral triple of the fuzzy torus. We…
Torquato and Stillinger conjectured an exponential improvement of Minkowski's classical lower bound on the maximal density of sphere packings in high-dimensional Euclidean space $\mathbb{R}^d$ using a pair-correlation-function optimization…
We develop a symplectic formulation of the Lagrangian Radon transform based on the transitive action of the symplectic group on the Lagrangian Grassmannian. This geometric framework naturally extends the classical notion of the marginals of…
In the space $\mathbb R^3$, for Robin parameter $L>0$, it is shown that there is a family of Schr\"odinger operators with penetrable toroidal solenoid and variable conductivity that approximates the magnetic Aharonov-Bohm operator with a…
The divergence of Feynman graph integrals is one of the central issues in the study of perturbative quantum field theories. A rigorous formulation of these integrals usually requires renormalization. In this paper, we prove that the Feynman…
We study a Nelson-type Hamiltonian describing a massive spinless non-relativistic particle moving in a planar soft quantum waveguide and linearly coupled to a massive scalar bosonic field. Our spectral analysis relies on comparing the…
We study a class of Friedrichs Hamiltonians, that is, operators describing an excited state coupled to a bath through a rank-one perturbation, in the case where the bath Hamiltonian has purely discrete spectrum. We consider sequences of…
We prove a conjecture formulated by Bolsinov, Konyaev and Matveev in [7] stating that, integrability of a system of hydrodynamic type ${\bf u}_t=A({\bf u}) {\bf u}_x$ with $\mathfrak{gl}$-regular $A$ at a point $p$ implies the vanishing of…
We construct an explicit embedding of the rank two Racah algebra $\mathfrak{R}_2$ into the rank two Jacobi algebra $\mathfrak{J}_2$. Working in the differential model of $\mathfrak{J}_2$ on the triangle, we recall that the subalgebra…
The author studies the inverse spectral problem of Sturm-Liouville operator on a star-like metric graph. At the vertex of this star-like graph, there are attached $m$ edges that imposed with non-local Sturm-Liouville operator satisfying…
Freed and Hopkins developed an ansatz for classifying interacting SPT phases using invertible field theories with a natural Free to Interacting (FTI) map from free fermion phases. This ansatz has been generalized to include crystalline…
We prove the redundancy of a family (the so-called melonic family) of large-$N$ moments in arbitrary tensor models. This reduces the number of independent entries in the positive semidefinite matrices that build the core of the tensor…
We revisit the proof of a $\mathfrak{bms}_3-$integrable hierarchy introduced in Fuentealba et al. (JHEP, 2018), using different structural methodologies. Specifically, from the variational complex on the ring of polynomial symbols, a…
In this paper, the corner Poisson structure of four-dimensional Palatini-Cartan gravity is derived. Building on the classical description of gravity on manifolds with boundary, specifically on the boundary constraint algebra, a pre- Dirac…
Operators invariant under a symmetry group are also invariant under any finite-index subgroup. The equivariant indices of such operators must be consistent under symmetry breaking. We use this principle to establish a canonical weak/strong…
We investigate the stationary Dirac equation associated with a generalized Kronig-Penney model in (N+1)-dimensional Clifford analysis. Away from the interaction sites, the free Dirac system is reformulated by introducing suitable…
We consider classical particles in the continuum in the grand canonical ensemble, with a stable, tempered and lower-regular pair potential and boundary conditions of uniformly bounded density. We prove that if the Lee--Yang zeros of the…
We highlight a simple congruence transform that shifts coupling parameters for Dirac operators with shell interactions. As one of the consequences, this leads to new observations concerning the self-adjointness and the infinite mass…
Formal $q$-Hamiltonian mechanics on the quantum plane is expressed through noncommuting coordinates and covariant $q$-derivatives, whereas its computable realization is usually written as an ordinary differential system involving Jackson…
\noindent Given an AKSZ theory $\mathbb{T}$ on a manifold $M$, with target a graded vector space $Y$, we formulate a 1-dimensional theory $\mathbb{t}$ on graphs (the ``first quantisation picture for $\mathbb{T}$''), whose partition…