Related papers: Constructing $\omega$-free Hardy fields
We show that all maximal Hardy fields are elementarily equivalent as differential fields, and give various applications of this result and its proof. We also answer some questions on Hardy fields posed by Boshernitzan.
We discuss the conjecture that every maximal Hardy field has the Intermediate Value Property for differential polynomials, and its equivalence to the statement that all maximal Hardy field are elementarily equivalent to the differential…
We study relative differential closure in the context of Hardy fields. Using our earlier work on algebraic differential equations over Hardy fields, this leads to a proof of a conjecture of Boshernitzan (1981): the intersection of all…
We define the universal exponential extension of an algebraically closed differential field and investigate its properties in the presence of a nice valuation and in connection with linear differential equations. Next we prove normalization…
We show that all maximal Hardy fields are elementarily equivalent as differential fields to the differential field $\mathbb T$ of transseries, and give various applications of this result and its proof.
We show that the sharp constant in the classical $n$-dimensional Hardy-Leray inequality can be improved for axisymmetric divergence-free fields, and find its optimal value. The same result is obtained for $n=2$ without the axisymmetry…
Differentially algebraic Hardy field extensions of short Hardy fields are short. This is proved in the more general setting of $H$-fields. As an application we extend a theorem of Rosenlicht (1981) by showing that each short asymptotic…
We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type inequality that takes…
In quantum logical terms, Hardy-type arguments can be uniformly presented and extended as collections of intertwined contexts and their observables. If interpreted classically those structures serve as graph-theoretic "gadgets" that enforce…
We deal with Dirac operators with external homogeneous magnetic fields. Hardy-type inequalities related to these operators are investigated: for a suitable class of transversal magnetic fields, we prove a Hardy inequality with the same best…
We begin a study of possibilities of describing hadrons in terms of monolocal fields which transform as proper Lorentz group representations decomposable into an infinite direct sum of finite-dimensional irreducible representations. The…
We show that maximal analytic Hardy fields are $\eta_1$ in the sense of Hausdorff. We also prove various embedding theorems about analytic Hardy fields. For example, the ordered differential field $\mathbb T$ of transseries is shown to be…
We prove that if an $\omega$-categorical structure has an $\omega$-categorical homogeneous Ramsey expansion, then so does its model-complete core.
We carry out the extension of the covariant Ostrogradski method to fermionic field theories. Higher-derivative Lagrangians reduce to second order differential ones with one explicit independent field for each degree of freedom.
In the single-field case, Horndeski provides the most general scalar-tensor theory with second-order field equations. By contrast, systematic multi-field extensions remain incomplete: while the general field equations for the bi-Horndeski…
This paper is a part of ongoing research on order positive fields started some years ago. We prove that the real closure of an order positive field even in non-Archimedean case is also order positive.
Morrey's classical inequality implies the H\"older continuity of a function whose gradient is sufficiently integrable. Another consequence is the Hardy-type inequality $$ \lambda\biggl\|\frac{u}{d_\Omega^{1-n/p}}\biggr\|_{\infty}^p\le…
We prove absolute continuity for an extended class of two-dimensional magnetic Hamiltonians that were initially studied by A. Iwatsuka. In particular, we add an electric field that is translation invariant in the same direction as the…
We introduce the spherical field formalism for free gauge fields. We discuss the structure of the spherical Hamiltonian for both general covariant gauge and radial gauge and point out several new features not present in the scalar field…
We derive necessary and sufficient conditions for large $N$ conformal field theories to have a universal free energy and an extended range of validity of the higher-dimensional Cardy formula. These constraints are much tighter than in two…