Related papers: Laplacians on discrete and quantum geometries
We show that the discrete anomaly constraints governing popular non-Abelian symmetries of use in (e.g.) flavoured, supersymmetric, and dark matter model building typically subdivide into two classes differentiated by the simple restrictions…
We provide a comprehensive classification of constraints and degrees of freedom for variational discrete systems governed by quadratic actions. This classification is based on the different types of null vectors of the Lagrangian two-form…
Weights are geometrical degrees of freedom that allow to generalise Lagrangian finite elements. They are defined through integrals over specific supports, well understood in terms of differential forms and integration, and lie within the…
This article provides a pedagogically oriented introduction to geometric (Clifford) calculus on pseudo-Riemannian manifolds. Unlike usual approaches to the topic, which rely on embedding the geometric algebra either within a tensor algebra…
We establish explicit operator norm bounds and essential self-adjointness criteria for discrete Hodge Laplacians on weighted graphs and simplicial complexes. For unweighted $d$-regular graphs we prove the universal estimate…
The presented paper is a review of papers on the microcosm physics geometrization in the last twenty years. These papers develop a new direction of the microcosm physics. It is so-called geometric paradigm, which is alternative to the…
A finite discrete graph is turned into a quantum (metric) graph once a finite length is assigned to each edge and the one-dimensional Laplacian is taken to be the operator. We study the dependence of the spectral gap (the first positive…
Let $X=G/H$ be a symmetric space for a real simple Lie group $G$, equipped with a $G$-invariant complex structure. Then, $X$ is a pseudo-Hermitian manifold, and in this geometric setting, higher Laplacians $L_m$ are defined for each…
Starting from a recently proposed linear formulation in terms of auxiliary fields, we study $n$-field generalizations of Born and Born-Infeld theories. In this description the Lagrangian is quadratic in the vector field strengths and the…
We consider Laplace operators on metric graphs, networks of one-dimensional line segments (bonds), with matching conditions at the vertices that make the operator self-adjoint. Such quantum graphs provide a simple model of quantum mechanics…
There is a deformation of the ordinary differential calculus which leads from the continuum to a lattice (and induces a corresponding deformation of physical theories). We recall some of its features and relate it to a general framework of…
We are interested in differential forms on mixed-dimensional geometries, in the sense of a domain containing sets of $d$-dimensional manifolds, structured hierarchically so that each $d$-dimensional manifold is contained in the boundary of…
Multisymplectic geometry is an adequate formalism to geometrically describe first order classical field theories. The De Donder-Weyl equations are treated in the framework of multisymplectic geometry, solutions are identified as integral…
Lattice quantum chromodynamics (QCD) will soon become the primary theoretical tool in rigorous studies of single- and multi-hadron sectors of QCD. It is truly ab initio meaning that its only parameters are those of standard model. The…
In perturbative gravity, it is straight-forward to characterize the two local degrees of freedom of the gravitational field in terms of a mode expansion of the linearized perturbation. In the non-perturbative regime, we are in a more…
We survey recent results in hermitian integral geometry, i.e. integral geometry on complex vector spaces and complex space forms. We study valuations and curvature measures on complex space forms and describe how the global and local…
We begin with a description of spacetime by a 4-dimensional cubic lattice $\sscript$. It follows from this framework that the the speed of light is the only nonzero instantaneous speed for a particle. The dual space $\sscripthat$…
We develop a Bochner theory and Bakry-Emery calculus for horizontal Laplacians associated with general Riemannian foliations. No bundle-like assumption on the metric, nor any total geodesicity or minimality condition on the leaves is…
After a brief survey of zeta function regularization issues and of the related multiplicative anomaly, illustrated with a couple of basic examples, namely the harmonic oscillator and quantum field theory at finite temperature, an…
We propose a coordinate-invariant geometric formulation of the GENERIC stochastic differential equation, unifying reversible Hamiltonian and irreversible dissipative dynamics within a differential-geometric framework. Our construction…