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The structure of classical electrodynamics based on the variational principle together with causality and space-time homogeneity is analyzed. It is proved that in this case the 4-potentials are defined uniquely. On the other hand, the…
It is shown that the topologies and nestings of the zero and nodal sets of random (Gaussian) band limited functions have universal laws of distribution. Qualitative features of the supports of these distributions are determined. In…
It is shown that the topologies and nestings of the zero and nodal sets of random (Gaussian) band limited functions have universal laws of distribution. Qualitative features of the supports of these distributions are determined. In…
We analyze the dynamics of gauge theories and constrained systems in general under small perturbations around a classical solution (background) in both Lagrangian and Hamiltonian formalisms. We prove that a fluctuations theory, described by…
We numerically study a one-dimensional system of $N$ classical localized planar rotators coupled through interactions which decay with distance as $1/r^\alpha$ ($\alpha \ge 0$). The approach is a first principle one (\textit{i.e.}, based on…
It is shown that the characteristics of the mesoscopic fluctuations in the conventional quantum-diffusion model and the model of the non-coherent (`classical') diffusion in media with long-range correlated disorder are quite similar in the…
Recently, a gauge theory of unified gravity [Rep. Prog. Phys. 88, 057802 (2025)] has been developed to extend the Standard Model to include gravity. Here we present unified gravity using the ordinary four-vector and tensor field notation of…
Liquid structure carries deep imprints of an inherent thermal invariance against a spatial transformation of the underlying classical many-body Hamiltonian. At first order in the transformation field the Noether theorem yields the local…
An uniform expansion of the Legendre functions of large indices are considered by using the WKB approach. We obtain the recurrent formula for the coefficients of uniform expansion and compare them with the uniform expansion of the Bessel…
In these lectures I talk about simplifications and universalities found in scattering amplitudes for gauge and gravity theories. In contrast to Ward identities, which are understood to arise from familiar symmetries of the classical action,…
We obtain within Fokker-Planck dynamics an explicit generalization of Einstein's relation between drag, diffusion and equilibrium distribution for a spatially homogeneous system, considering both the transverse and longitudinal diffusion…
The effective four-dimensional, linearised gravity of a brane world model with one extra dimension and a single brane is analysed. The model includes higher order curvature terms (such as the Gauss-Bonnet term) and a conformally coupled…
Color-ordered amplitudes in gauge theories satisfy non-linear identities involving amplitude products of different helicity configurations. We consider the origin of such identities and connect them to the Kawai-Lewellen-Tye (KLT) relations…
Graph rules for the linked cluster expansion of the Legendre effective action $\Gamma[\phi]$ are derived and proven in $D\geq 2$ Euclidean dimensions. A key aspect is the weight assigned to articulation vertices which is itself shown to be…
Following the recent work [13] fulfilled in the discrete case, we pro- vide in this paper new intertwining relations for semigroups of one-dimensional diffusions. Various applications of these results are investigated, among them the famous…
The phenomenon in the essence of classical uncertainty principles is well known since the thirties of the last century. We introduce a new phenomenon which is in the essence of a new notion that we introduce: "Generalized Uncertainty…
We develop differential calculus and gauge theory on a finite set G. An elegant formulation is obtained when G is supplied with a group structure and in particular for a cyclic group. Connes' two-point model (which is an essential…
It is well-known that separation of variables in 2nd order partial differential equations (PDEs) for physical problems with spherical symmetry usually leads to Cauchy's differential equation for the radial coordinate and Legendre's…
The quantum geometric tensor (QGT) provides nontrivial bounds among physical quantities, as exemplified by the metric-curvature inequality. In this paper, we investigate various bounds for different observables through certain…
We show how the Legendre transforms of the fundamental thermodynamic relation can be used to introduce different statistical ensembles.