Related papers: Renormalization of potentials and generalized cent…
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 provide a simple, general argument to obtain improvements of concentration-type inequalities starting from improvements of their corresponding isoperimetric-type inequalities. We apply this argument to obtain robust improvements of the…
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 Polynomial Freiman-Ruzsa conjecture is one of the central open problems in additive combinatorics. If true, it would give tight quantitative bounds relating combinatorial and algebraic notions of approximate subgroups. In this note, we…
By the Hardy-Littlewood-Sobolev theorem the classical Riesz potential is bounded on Lebesgue spaces. E. Nakai and H. Sumitomo [16] extended that theorem to the Orlicz spaces. We introduce generalized potential operators on commutative…
We generalize the concept of Borel resummability and renormalons to a quantum field theory with an arbitrary number of fields and couplings, starting from the known notion based on the running coupling constants. An approach to identify the…
We classify the local, polynomial, unitary gauge theories that violate Lorentz symmetry explicitly at high energies and are renormalizable by weighted power counting. We study the structure of such theories and prove that renormalization…
Generalisations of the relativistic ideal Ohm's law are presented that include specific dynamical features of the current carrying particles in a plasma. Cases of interest for space and laboratory plasmas are identified where these…
This is a lecture note on the renormalization group theory for field theory models based on the dimensional regularization method. We discuss the renormalization group approach to fundamental field theoretic models in low dimensions. We…
The quantum-mechanical D-dimensional inverse square potential is analyzed using field-theoretic renormalization techniques. A solution is presented for both the bound-state and scattering sectors of the theory using cutoff and dimensional…
In this article we derive the expression of \textit{renormalized energies} for unit-valued harmonic maps defined on a smooth bounded domain in \(\mathbb{R}^2\) whose boundary has several connected components. The notion of renormalized…
We analyse the power counting renormalizability of the quantum field theory of Einstein or Einstein-Gauss-Bonnet gravity in D+2 dimensional Lifshitz spacetime. We show the spectral dimension becomes 2+(D/z) at the UV region where z is the…
Many star bodies have convex subsets with approximately the same Gaussian measure (of the complement). Inspired by this phenomenon, and in connection with the randomized Dvoretzky theorem for Lorentz spaces, we derive bounds on the…
We show that the regularized Riesz $\a$-energy for closed submanifolds $M$ in $\RR^n$ blows up as $M$ degenerates to have double points if $\a\le-2\dim M$. This gives theoretical foundation of numerical experiments to evolve surfaces to…
We consider the inverse problem of reconstructing general solutions to the Helmholtz equation on some domain $\Omega$ from their values at scattered points $x_1,\dots,x_n\subset \Omega$. This problem typically arises when sampling acoustic…
A method is presented which allows for the renormalization of the self-potential for a scalar point charge at rest in static curved space-time. The method is suitable for the scalar field with arbitrary mass $m$ and coupling to the scalar…
Cosmological models arising from a generalized compactification of Einstein gravity are derived. It is shown that a redefinition of the moduli fields reduces the system to a set of massless fields and a single field with a single…
We consider harmonic functions in the unit ball of $\mathbb{R}^{n+1}$ that are unbounded near the boundary but can be estimated from above by some (rapidly increasing) radial weight $w$. Our main result gives some conditions on $w$ that…
This is a survey on renormalisation in the locality setup highlighting the role that locality morphisms can play for renormalisation purposes. Having set up a general framework to build regularisation maps, we illustrate renormalisation by…
Inequalities for Riesz potentials are well-known to be equivalent to Sobolev inequalities of the same order for domain norms ``far" from $L^1$, but to be weaker otherwise. Recent contributions by Van Schaftingen, by Hernandez, Rai\c{t}\u{a}…