Related papers: KAM for the Klein Gordon equation on $\mathbb S^d$
We consider the codimension one asymptotic stability problem for the soliton of the focusing cubic Klein-Gordon equation on the line under even perturbations. The main obstruction to full asymptotic stability on the center-stable manifold…
We introduce an embedding of the Klein-Gordon equation into a pair of coupled equations that are first-order in time. The existence of such an embedding is based on a positivity property exhibited by the Klein-Gordon equation. These coupled…
Quasi-periodic solutions with Liouvillean frequency of forced nonlinear Schr\"odinger equation are constructed. This is based on an infinite dimensional KAM theory for Liouvillean frequency.
We are interested in the numerical solution of coupled nonlinear partial differential equations (PDEs) in two and three dimensions. Under certain assumptions on the domain, we take advantage of the Kronecker structure arising in standard…
For $d \geq 2, \ D \geq 1$, let $\mathscr{P}_{d,D}$ denote the set of all degree $d$ polynomials in $D$ dimensions with real coefficients without linear terms. We prove that for any Calder\'{o}n-Zygmund kernel, $K$, the maximally modulated…
The Klein Gordon equation was the first attempt at unifying special relativity and quantum mechanics. While initially discarded this equation of "many fathers" can be used in understanding spinless particles that consequently led to the…
The parametric equations of KAM tori for a quasi integrable system, are shown to be one point Schwinger functions of a suitable euclidean quantum field theory on the torus. KAM theorem is equivalent to a ultraviolet stability theorem. A…
A quantum kinetic theory of the linear response to an electric field is provided from a controlled expansion of the Keldysh theory at leading order, for a multiband electron system with weak scalar disorder. The response is uniquely…
We consider quasi-linear, Hamiltonian perturbations of the cubic Schr\"odinger and of the cubic (derivative) Klein-Gordon equations on the $d$ dimensional torus. If $\varepsilon\ll1$ is the size of the initial datum, we prove that the…
The recent results in QCD at low energies are reported. The theoretical analysis of hadronic tau-decay is performed in complex q^2-plane. The terms of perturbation theory (PT) up to alpha^3_s are accounted, the terms of operator product…
We study the effect of linear transformations on quantum fields with applications to vertex operator presentations of symmetric functions. Properties of linearly transformed quantum fields and corresponding transformations of…
We propose a covariant definition of the fractional Klein-Gordon equation with long-range interactions independent of the metric of the underlying manifold. As an example we consider the fractional Klein-Gordon equation on AdS$_{2+1}$,…
We consider a two-dimensional integrable Hamiltonian system with a vector and scalar potential in quantum mechanics. Contrary to the case of a pure scalar potential, the existence of a second order integral of motion does not guarantee the…
By exploiting estimates on Bloch functions obtained in a previous paper, we prove decay estimates for Klein Gordon equations with a time independent potential periodic in space in 1D and with generic mass
We prove a quantitative version of Gordon's Theorem concerning absence of eigenvalues for Jacobi matrices and Sturm-Liouville operators with complex coefficients.
The quasi-potential is a key concept of the Large Deviation Theory for Stochastic Differential Equations (SDEs). Once the quasi-potential with respect to an attractor of the corresponding deterministic system is found, one can readily…
We prove existence and multiplicity of Cantor families of small amplitude time periodic solutions of completely resonant Klein-Gordon equations on the sphere $\mathbb{S}^3$ with quadratic, cubic and quintic nonlinearity, regarded as toy…
A strict proof of equivalence between Duffin-Kemmer-Petiau (DKP) and Klein-Gordon (KG) theories is presented for physical S-matrix elements in the case of charged scalar particles interacting in minimal way with an external or quantized…
We extend the three-dimensional noncommutative relations of the positions and momenta operators to those in the four dimension. Using the Bopp shift technique, we give the Heisenberg representation of these noncommutative algebras and endow…
We study the Klein-Gordon equation in one spatial and one temporal dimension. Physically, this equation describes the wave function of a relativistic spinless boson with positive rest mass. Mathematically, this is the most elementary…