Related papers: Yang-Mills Meets Data
A new approach extending the concept of geometric phases to adiabatic open quantum systems described by density matrices (mixed states) is proposed. This new approach is based on an analogy between open quantum systems and dissipative…
Yang-Mills-Higgs theory, being the standard-model Higgs sector for a suitable choice of gauge and custodial group, offers a rich set of physics. In particular, in some region of its parameter space it has QCD-like behavior, while in some…
Let $G$ be an infinite, edge- and vertex-weighted graph with certain reasonable restrictions. We construct the heat kernel of the associated Laplacian using an adaptation of the parametrix approach due to Minakshisundaram-Pleijel in the…
We introduce a geometric construction of a gauge field theory of a complex adaptive system. It is based on a suitable simplicial formulation of a discrete geometry that manifests relevant properties valid in the classical differentiable…
The kinematic algebra of Yang-Mills theory can be understood in the framework of homotopy algebras: the $L_{\infty}$ algebra of Yang-Mills theory is the tensor product of the color Lie algebra and a kinematic space that carries a…
This paper gives a construction, using heat kernels, of differential forms on the moduli space of metrised ribbon graphs, or equivalently on the moduli space of Riemann surfaces with boundary. The construction depends on a manifold with a…
In this talk, we discuss a number of recent calculations aimed at determining the spectral functions corresponding to various components of the energy momentum tensor in high-temperature SU(N) Yang-Mills theory. The computations reviewed…
We propose a new framework for simulating $\text{U}(k)$ Yang-Mills theory on a universal quantum computer. This construction uses the orbifold lattice formulation proposed by Kaplan, Katz, and Unsal, who originally applied it to…
We construct a gauge theory based on principal bundles $\mathcal{P}$ equipped with a right $\mathcal{G}$-action, where $\mathcal{G}$ is a Lie group bundle instead of a Lie group. Due to the fact that a $\mathcal{G}$-action acts fibre by…
Geometric data analysis and learning has emerged as a distinct and rapidly developing research area, increasingly recognized for its effectiveness across diverse applications. At the heart of this field lies curvature, a powerful and…
Results regarding off-diagonal Gaussian upper heat kernel bounds on discrete weighted graphs with possibly unbounded geometry are summarized and related. After reviewing uniform upper heat kernel bounds obtained by Carlen, Kusuoka, and…
A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…
This work incorporates the multi-modality of the data distribution into a Gaussian Process regression model. We approach the problem from a discriminative perspective by learning, jointly over the training data, the target space variance in…
We present a new tool for data analysis: persistence discrete homology, which is well-suited to analyze filtrations of graphs. In particular, we provide a novel way of representing high-dimensional data as a filtration of graphs using…
An ansatz is presented for a possible non-associative deformation of the standard Yang-Mills type gauge theories. An explicit algebraic structure for the deformed gauge symmetry is put forward and the resulting gauge theory developed. The…
We unify three approaches within the vast body of gauge-theory research that have independently developed distinct representations of a geometrical surface-like structure underlying the vector-potential. The three approaches that we unify…
The status of several representative gauge theories on various quantum space-times, mainly focusing on Yang-Mills type extensions together with a few matrix model formulations is overviewed. The common building blocks are derivation based…
We construct explicit BPS and non-BPS solutions of the Yang-Mills equations on noncommutative spaces R^{2n}_theta x G/H which are manifestly G-symmetric. Given a G-representation, by twisting with a particular bundle over G/H, we obtain a…
A specific class of gauge theories is geometrically described in terms of fermions. In particular, it is shown how the geometrical frame presented naturally includes spontaneous symmetry breaking of Yang-Mills gauge theories without making…
We explain the concepts of computational statistical physics which have proven very helpful in the study of Yang-Mills integrals, an ubiquitous new class of matrix models. Issues treated are: Absolute convergence versus Monte Carlo…