Related papers: Renormalization Theory in the Electrostatic and Ve…
The quantization of the electrical charge in the electrodynamics and of the hypercharge in the standard model are imposed in the theory based not on theoretical arguments but on the experimental observations. In this paper we propose a…
In the calculation of quantum-mechanical singular-potential scattering, one encounters divergence. We suggest three renormalization schemes, dimensional renormalization, analytic continuation approach, and minimal-subtraction scheme to…
We illustrate the dimensional regularization technique using a simple problem from elementary electrostatics. We contrast this approach with the cutoff regularization approach, and demonstrate that dimensional regularization preserves the…
Renormalization ideas can profitably be exploited in conjunction with the superposition principle of boundary conditions in the description of model independent and universal scaling features of the singular and long range Van der Waals…
We describe a class of unified theories of electromagnetism and gravity. The Lagrangian is of the BF type, with a potential for the B-field, the gauge group is U(2) (complexified). Given a choice of the potential function the theory is a…
Variational methods have become an important kind of methods in signal and image restoration - a typical inverse problem. One important minimization model consists of the squared $\ell_2$ data fidelity (corresponding to Gaussian noise) and…
The Pauli--Villars regularization procedure confirms and sharpens the conclusions reached previously by covariant point splitting. The divergences in the stress tensor of a quantized scalar field interacting with a static scalar potential…
The old problem of a singular, inverse square potential in nonrelativistic quantum mechanics is treated employing a field-theoretic, functional renormalization method. An emergent contact coupling flows to a fixed point or develops a limit…
This PhD thesis is devoted to show that differential renormalization is a simple and useful renormalization method that we can use when dealing with gauge theories. In this work, it is shown how the one-loop results of Constraint…
The estimation law of unknown parameters vector ${\theta}$ is proposed for one class of nonlinearly parametrized regression equations $y\left( t \right) = \Omega \left( t \right)\Theta \left( \theta \right)$. We restrict our attention to…
As applied to quantum theories, the program of renormalization is successful for `renormalizable models' but fails for `nonrenormalizable models'. After some conceptual discussion and analysis, an enhanced program of renormalization is…
We study the information content of the reduced density matrix of a region in quantum field theory that cannot be recovered from its subregion density matrices. We reconstruct the density matrix from its subregions using two approaches:…
Some quantum mechanical potentials, singular at short distances, lead to ultraviolet divergences when used in perturbation theory. Exactly as in quantum field theories, but much simpler, regularization and renormalization lead to finite…
Electric charge, as defined in the Thomson limit of the electron--photon interaction vertex, is renormalized to all orders both in the Standard Model and in any spontaneously broken gauge theory with gauge group GxU(1) with a group factor…
This is the first in a series of papers addressing the phenomenon of dimensional transmutation in nonrelativistic quantum mechanics within the framework of dimensional regularization. Scale-invariant potentials are identified and their…
We discuss a couple of simple quasistatic electromagnetic systems in which the density of electromagnetic linear momentum can be easily computed. The examples are also used to illustrate how the total electromagnetic linear momentum, which…
The renormalization group is extended to cases where several heavy particles are decoupled at the same time. This involves large logarithms which are scale-invariant and so cannot be eliminated by a change of renormalization scheme. A set…
Using a renormalization approach, we study the asymptotic limit distribution of the maximum value in a set of independent and identically distributed random variables raised to a power q(n) that varies monotonically with the sample size n.…
The importance and usefulness of renormalization are emphasized in nonrelativistic quantum mechanics. The momentum space treatment of both two-body bound state and scattering problems involving some potentials singular at the origin…
Using resummation in perturbation theories at finite temperature or in non-equilibrium is unavoidable to obtain consistent results. Resummation, however, is often in conflict with renormalization. In this talk we give two possible solutions…