Related papers: Towards sharp regularity: Full-dimensional tori in…
We explore the convergence/divergence of the normal form for a singularity of a vector field on $\C^n$ with nilpotent linear part. We show that a Gevrey-$\alpha$ vector field $X$ with a nilpotent linear part can be reduced to a normal form…
This work introduces topological regularization as a framework for handling ultraviolet divergences in quantum field theory, reinterpreting infinities as topological obstructions at spacetime boundaries. Through geometric compactification…
We study the stability and breakup of invariant tori in Hamiltonian flows using a combination of Kolmogorov-Arnold-Moser (KAM) theory and renormalization-group techniques. We implement the scheme numerically for a family of Hamiltonians…
Let $X$ be a $G$-homogeneous space over a number field $k$ such that $X\cong G_\gamma\backslash G$. Here, $G$ is a simply connected semisimple group over $k$ and $\gamma\in G(k)$ whose centralizer $G_\gamma$ is a maximal torus in $G$ which…
Using standard field theoretical techniques, we survey pure Yang-Mills theory on the noncommutative torus, including Feynman rules and BRS symmetry. Although in general free of any infrared singularity, the theory is ultraviolet divergent.…
We regularize in a continuous manner the path integral of QED by construction of a non-local version of its action by means of a regularized form of Dirac's $\delta$ functions. Since the action and the measure are both invariant under the…
We consider nonlinear Schr\"odinger equations on flat tori satisfying a simple and explicit Diophantine non-degeneracy condition. Provided that the nonlinearity contains a cubic term, we prove the almost global existence and stability of…
We provide an arithmetic condition weaker then the Bryuno condition for which it is possible to apply a KAM scheme in dimension greater then one. The KAM scheme will be provided in the setting of linearization of analytic diffeomorphisms of…
In this work we study a warped five-dimensional (5D) model with ultraviolet (UV) and infrared (IR) branes, that solves the hierarchy problem with a fundamental 5D Planck scale $M$, and curvature parameter $k$, of the order of the 4D Planck…
We consider the standard family of area-preserving twist maps of the annulus and the corresponding KAM curves. Addressing a question raised by Kolmogorov, we show that, instead of viewing these invariant curves as separate objects, each of…
This paper investigates Nekhoroshev-type stability for solutions of ultra-differentiable regularity in Schr\"odinger equations with non-local nonlinear terms, employing the method of rational normal forms. We establish the first rigorous…
The calculation of loop amplitudes with parity violation or spin effects within dimensional regularization needs a consistent definition of gamma5. Also loop calculations in supersymmetric theories need a consistent definition of gamma5. In…
We investigate the regularity of the viscosity solutions to a class of degenerate/singular fully nonlinear elliptic equations with Hamiltonian terms. To overcome the difficulty caused by the simultaneous presence of the general…
When a Gevrey smooth perturbation is applied to a quasi-convex integrable Hamiltonian, it is known that the KAM invariant tori that survive are sticky, that is, doubly exponentially stable. We show by examples the optimality of this…
The radiative induction of the CPT and Lorentz violating Chern-Simons (CS) term is reassessed. The massless and massive models are studied. Special attention is given to the preservation of gauge symmetry at higher orders in the background…
In this paper we prove the existence of quasi-periodic, small-amplitude, solutions for quasi-linear Hamiltonian perturbations of the non-linear Schroedinger equation on the torus in presence of a quasi-periodic forcing. In particular we…
This paper serves as a first foray on regularisation for planar vector fields. Motivated by singularities in celestial mechanics, the block regularisation of a generic class of degenerate singularities is studied. The paper is concerned…
The monotonicity-based approach has become one of the fundamental methods for reconstructing inclusions in the inverse problem of electrical impedance tomography. Thus far the method has not been proven to be able to handle extreme…
In this paper, it is proved that the infinite KAM torus with prescribed frequency exists in a sufficiently small neighborhood of a given $ I^{0}$ for nearly integrable and analytic Hamiltonian system $ H(I,\theta) = H_{0}(I)+ \epsilon…
The disadvantage of `traditional' multidimensional continued fraction algorithms is that it is not known whether they provide simultaneous rational approximations for generic vectors. Following ideas of Dani, Lagarias and Kleinbock-Margulis…