Related papers: Spectral perturbation theory and the two weights p…
Increasingly accurate observations are driving theoretical cosmology toward the use of more sophisticated descriptions of matter and the study of nonlinear perturbations of FL cosmologies, whose governing equations are notoriously…
Using the principles of the modern scattering amplitudes programme, we develop a formalism for constructing the amplitudes of three-dimensional topologically massive gauge theories and gravity. Inspired by recent developments in four…
We explore perturbative double field theory about time-dependent (cosmological) backgrounds to cubic order. To this order the theory is consistent in a weakly constrained sense, so that for a toroidal geometry it encodes both momentum and…
We consider an application of a general theory for cavities with point-like perturbations for a rectangular shape. Hereby we concentrate on experimental wave patterns obtained for nearly degenerate states. The nodal lines in these patterns…
It is shown how cosmological perturbation theory arises from a fully quantized perturbative theory of quantum gravity. Central for the derivation is a non-perturbative concept of gauge-invariant local observables by means of which…
We derive cosmological soft theorems for solids coupled to gravity. To this end, we first derive all cosmological adiabatic modes for solids, which display the interesting novelty of non-vanishing anisotropic stresses on large scales. Then,…
This paper is the first in a series of three which attempt to resolve the difficulties that have plagued the $NN-\pi NN$ problem for the past ten years. Various theoretical inconsistencies in the current formulation have been pointed out…
Recent work in the literature has found a suppression or, instead, an enhancement of the Cosmic Microwave Background power spectrum in quantum gravity, although the effect is too small to be observed, in both cases. The present paper…
The celebrated Weinberg theorem in cosmological perturbation theory states that there always exist two adiabatic scalar modes in which the comoving curvature perturbation is conserved on super-horizon scales. In particular, when the…
In cosmological perturbation theory a first major step consists in the decomposition of the various perturbation amplitudes into scalar, vector and tensor perturbations, which mutually decouple. In performing this decomposition one uses --…
A covariant, global, variational framework for perturbations in field theories is presented. Perturbations are obtained as vertical vector fields on the configuration bundle and they drag, exactly, solution into solutions. The flow of a…
Self-adjoint boundary problems for the equation $y^{(4)}-\lambda\rho y=0$ with generalized derivative $\rho\in W_2^{-1}[0,1]$ of self-similar Cantor type function as a weight are considered. Using the oscillating properties of the…
The main goal of this paper is to prove a two-weight criteria for multidimensio-nal Hardy type operator from weighted Lebesgue spaces into $p$-convex weighted Banach function spaces. Analogously problem for the dual operator is considered.…
We study perturbative general relativity with a two-form and a dilaton using the double field theory formulation which features explicit index factorisation at the Lagrangian level. Explicit checks to known tree level results are performed.…
In the q-deformed theory the perturbation approach can be expressed in terms of two pairs of undeformed position and momentum operators. There are two configuration spaces. Correspondingly there are two q-perturbation Hamiltonians, one…
We report a two-dimensional (2D) gravitating kink model, for which both the background field equations and the linear perturbation equation are exactly solvable. The background solution describes a sine-Gordon kink that interpolating…
Louis de Broglie's celebrated hypothesis transfers a problem of representation of optics to the quantum theories. Let us suppose that the fact that originated the problem in optics is the following, "The images obtained by optical…
We consider the problem of variation of spectral subspaces for linear self-adjoint operators under off-diagonal perturbations. We prove a number of new optimal results on the shift of the spectrum and obtain (sharp) estimates on the norm of…
In the 1970s Muckenhoupt and Wheeden made several conjectures relating two weight norm inequalities for the Hardy-Littlewood maximal operator to such inequalities for singular integrals. Using techniques developed for the recent proof of…
In the present paper, we consider the Cauchy problem of the system of quadratic derivative nonlinear Schr\"odinger equations for the spatial dimension $d=2$ and $3$. This system was introduced by M. Colin and T. Colin (2004). The first…