Related papers: Do Potential Fields Develop Current Sheets Under S…
We study the structure of an algebraically closed field with extra function resembling the classical exponentiation on complex numbers.
We demonstrate that any k*-expansive vector field on a closed manifold exhibits rescaling expansiveness. This enhances the principal outcome outlined in \cite{a}. The verification of this assertion hinges on the introduction and exploration…
The question if conserved currents can be sensibly defined in supersymmetric minisuperspaces is investigated in this essay. The objective is to employ exclusively the differential equations obtained {\em directly} from the Lorentz and…
A selection of open problems in the theory of composites is presented. Particular attention is drawn to the question of whether two-dimensional, two-phase, composites with general geometries have the same set of possible effective tensors…
In String Gas Cosmology, the simplest shape modulus fields are naturally stabilized by taking into account the presence of string winding and momentum modes. We determine the resulting effective potential for these fields and show that it…
A classification of stable singular points on world sheets of open relativistic strings is carried out.
The principles of a previously developed formalism for the covariant treatment of multi-scalar fields for which (as in a nonlinear sigma model) the relevant target space is not of affine type -- but curved -- are recapitulated. Their…
We use a localization procedure to weaken the growth assumptions of Royer [8], Miclo [4] and Zitt [9] concerning the continuous-time simulated annealing in $\mathbf{R}^d$. We show that a transition occurs for potentials growing like $a \log…
We study in this paper the sufficient conditions for enhanced continuity of random fields, i.e. such that the modulus of its continuity allows the factorable representation by the product of random variable on the deterministic module of…
Some of the recent developments in the theory of random surfaces and simplicial quantum gravity is reviewed. For 2d quantum gravity this includes the failure of Regge calculus, our improved understanding of the $c>1$ regime, some surprises…
We examine models in which the accelerated expansion of the universe is driven by a scalar field rolling near an inflection point in the potential. For the simplest such models, in which the potential is of the form V(\phi) = V_0 + V_3…
The hypothesis is rapidly gaining popularity that the dark energy pervading our universe is extra-repulsive ($-p>\rho$). The density of such a substance(usually called phantom energy) grows with the cosmological expansion and may become…
The relativistic generalization of the broken continuity equation that describes spin currents is exploited in general material media. The field theoretical techniques for the usual U(1) gauge theory with fermions in material media is…
It is one of the main properties of uniformly hyperbolic dynamics that points of two distinct trajectories cannot be uniformly close one to another. This characteristics of hyperbolic dynamics is called expansivity. Hirsch, Pugh and Shub,…
Effective field theories consistent with quantum gravity obey surprising finiteness constraints, appearing in several distinct but interconnected forms. In this work we develop a framework that unifies these observations by proposing that…
In our previous paper, we established Northcott's theorem for height functions over finitely generated fields. Unfortunately, Northcott's theorem on finitely generated fields does not hold in general. Actually, it depends on the choice of a…
We argue that the finiteness of quantum gravity amplitudes in fully compactified theories (at least in supersymmetric cases) leads to a bottom-up prediction for the existence of non-trivial dualities. In particular, finiteness requires the…
We show that the recently proposed weak gravity conjecture\cite{AMNV0601} can be extended to a class of scalar field theories. Taking gravity into account, we find an upper bound on the gravity interaction strength, expressed in terms of…
A corrector theory for the strong approximation of gradient fields inside periodic composites made from two materials with different power law behavior is provided. Each material component has a distinctly different exponent appearing in…
We review the developments in the past twenty years (which are based on our deformation philosophy of physical theories) dealing with elementary particles composed of singletons in anti De Sitter space-time. The study starts with the…