Related papers: From $p$-adic to Archimedean Physics: Renormalizat…
We perform rigorously the charge renormalization of the so-called reduced Bogoliubov-Dirac-Fock (rBDF) model. This nonlinear theory, based on the Dirac operator, describes atoms and molecules while taking into account vacuum polarization…
If phi(z) is a rational function on P^1 of degree at least 2 with coefficients in a number field k, we compute the homogeneous transfinite diameter of the v-adic filled Julia sets of phi for all places v of k by introducing a new quantity…
In this paper, a new formulation for the three dimensional Euler equations is derived. Since the Euler system is hyperbolic-elliptic coupled in a subsonic region, so an effective decoupling of the hyperbolic and elliptic modes is essential…
We pose and solve an inverse problem for the classical field equations that arise in the Standard Model of particle physics. Our main result describes natural conditions on the representations, so that it is possible to recover all the…
The particle creation by the so-called peak electric field is considered. The latter field is a combination of two exponential parts, one exponentially increasing and another exponentially decreasing. We find exact solutions of the Dirac…
Given a countable residually finite group $\Gamma$, we write $\Gamma_n \to e$ if $(\Gamma_n)$ is a sequence of normal subgroups of finite index such that any infinite intersection of $\Gamma_n$'s contains only the unit element $e$ of…
Over the past decades, many authors advertised models on complexified spacetime algebras for use in describing gravity. This work aims at providing phenomenological support to such claims, by introducing a one-parameter real phase $\alpha$…
For each prime $p$, a Vladimirov operator with a positive exponent specifies a $p$-adic diffusion equation and a measure on the Skorokhod space of $p$-adic paths. The product, $P$, of these measures with fixed exponent is a probability…
In previous works in this series we focussed on Hamiltonian renormalisation of free field theories in all spacetime dimensions or interacting theories in spacetime dimensions lower than four. In this paper we address the Hamiltonian…
In this article we have developed a formalism to obtain the Schr$\ddot{\rm{o}}$dinger equation for a particle in a frame undergoing an uniform acceleration in an otherwise flat Minkowski space-time geometry. We have presented an exact…
Point-particle dynamics is reformulated as a field theory. This is achieved by using the unfolded dynamics approach that makes it possible to give dynamical interpretation to the concept of physical dimension which is 1 for a point particle…
In terms of the relational approach to space-time geometry and physical interactions, we show that the Dirac equation for a free fermion in the momentum representation can be obtained starting from a binary system of complex relations…
Singular potentials (the inverse-square potential, for example) arise in many situations and their quantum treatment leads to well-known ambiguities in choosing boundary conditions for the wave-function at the position of the potential's…
The Renormalization Group Flow Equations of the Scalar-QED model near Planck's scale are computed within the framework of the average effective action. Exact Flow Equations, corrected by Einstein Gravity, for the running self-interacting…
We derive Euler equations from a Hamiltonian microscopic dynamics. The microscopic system is a one-dimensional disordered harmonic chain, and the dynamics is either quantum or classical. This chain is an Anderson insulator with a symmetry…
Adapting the notion of the spectrum $\Sigma_a$ for an element $a$ in an ultrametric Banach algebra (as defined by Berkovich), we introduce and briefly study the Berkovich spectrum $\sigma^{Ber}_R(u)$ of an element $u$ in a Banach ring $R$.…
We study the isospectrality problem for a relativistic free quantum particle, described by the Dirac Hamiltonian, confined in a one-dimensional ring with a junction. We analyze all the self-adjoint extensions of the Hamiltonian in terms of…
Given a finite morphism $\varphi:Y\to X$ of quasi-smooth Berkovich curves over a complete, algebraically closed field $k$ of characteristic $0$, we prove a Riemann-Hurwitz formula relating their Euler-Poincar\'e characteristics (calculated…
We study the gradient flow of the potential energy on the infinite-dimensional Riemannian manifold of spatial curves parametrized by the arc length, which models overdamped motion of a falling inextensible string. We prove existence of…
It is shown that the $p$-adic Banach spaces introduced by Emerton are isomorphic to the cohomology groups of the sheaf of continuous $\Q_{p}$-valued functions on a certain space. Some applications of this result are discussed.