Related papers: Studying the gradient flow coupling in the Schr\"o…
We derive the system of differential equations for the gradient flow characterizing the training process of linear in-context learning in full generality. Next, we explore the geometric structure of the gradient flows in two instances,…
For the first time, the general nonlinear Schr\"odinger equation is investigated, in which the chromatic dispersion and potential are specified by two arbitrary functions. The equation in question is a natural generalization of a wide class…
We consider a scalar Euclidean QFT with interaction given by a bounded, measurable function $V$ such that $V^{\pm}:=\lim_{w\to \pm\infty}V(w)$ exist. We find a field renormalization such that all the $n$-point connected Schwinger functions…
We analyze the approach to chiral symmetry breaking in QCD at finite temperature, using the functional renormalization group. We compute the running gauge coupling in QCD for all temperatures and scales within a simple truncated…
Through appropriate projections of an exact renormalization group equation, we study fixed points, critical exponents and nontrivial renormalization group flows in scalar field theories in $2<d<4$. The standard upper critical dimensions…
We review the present knowledge for $\alpha_s$, the fundamental coupling underlying the interactions of quarks and gluons in QCD. The dependence of $\alpha_s(Q^2)$ on momentum transfer $Q$ encodes the underlying dynamics of hadron physics…
We analytically compute the five-loop term in the beta function which governs the running of $\alpha_s$ --- the quark-gluon coupling constant in QCD. The new term leads to a reduction of the theory uncertainty in $\alpha_s$ taken at the…
In this note we first set up an analogy between spin and vorticity of a perfect 2d-fluid flow, based on the Borel-Weil contruction of the irreducible unitary representations of SU(2), and looking at the Madelung-Bohm velocity attached to…
The effective average action of Yang-Mills theory is analyzed in the framework of exact renormalization group flow equations. Employing the background-field method and using a cutoff that is adjusted to the spectral flow, the running of the…
In models with large additional dimensions, the GUT scale can be lowered to values accessible by future colliders. Due to modification of the loop corrections from particles propagating into the extra dimensions, the logarithmic running of…
{}From an accurate determination of the inter-quark potential, one can study the running coupling constant for a range of $R$-values and hence estimate the scale $\Lambda_{\msbar} $. Detailed results are presented for $SU(3)$ pure gauge…
We study SU(2) lattice gauge theory with two flavours of Dirac fermions in the adjoint representation. We measure the running of the coupling in the Schroedinger Functional (SF) scheme and find it is consistent with existing results. We…
We present a systematic decomposition of QCD splitting functions into scalar dipole radiators and pure splitting remainders up to second order in the strong coupling. The individual components contain terms that are formally sub-leading in…
A short overview of studies of strong coupling problems in hadron physics is presented. The Schwinger-Dyson/Bethe-Salpeter approach in the continuum allows the perturbative regime to be connected to the world of strong coupling that…
Gradient flow has been proposed in the lattice community as a tool to reduce the sensitivity of operator correlation functions to noisy UV fluctuations. We test perturbatively under what conditions doing so may contaminate the results. To…
We prove an integral formula for the spectral flow of differentiable loops of unitaries of the form ${\rm Id}+$Schatten. Our formula is in terms of a regularised winding number, expressed in terms of exact differential forms, and we show…
This study presents numerical simulations and experiments considering the flow of an electrically conducting fluid inside a cube driven by a rotating magnetic field (RMF). The investigations are focused on the spin-up, where a liquid metal…
We present a one-loop calculation of a gauge invariant QCD beta function. Using both momentum and temperature renormalization group equations we investigate the running coupling in the magnetic sector as a function of temperature and…
We consider a general formulation of gradient flow evolution for problems whose natural framework is the one of metric spaces. The applications we deal with are concerned with the evolution of {\it capacitary measures} with respect to the…
On the universal bundle of unit spinors we study a natural energy functional whose critical points, if dim M \geq 3, are precisely the pairs (g, {\phi}) consisting of a Ricci-flat Riemannian metric g together with a parallel g-spinor…