相关论文: Quantum stability of non-linear wave type solution…

In the present work, we introduce a new $\mathcal{PT}$-symmetric variant of the Klein-Gordon field theoretic problem. We identify the standing wave solutions of the proposed class of equations and analyze their stability. In particular, we…

Using the effective potential approach for composite operators we have formulated the quantum model of the QCD vacuum. It is based on the existence and importance of the nonperturbative $q^{-4}$-type dynamical, topologically nontrivial…

In this work we prove the existence of standing-wave solutions to the scalar non-linear Klein-Gordon equation in dimension one and the stability of the ground-state, the set which contains all the minima of the energy constrained to the…

We apply spectral stability theory to investigate nonlinear gravity waves in the atmosphere. These waves are determined by modulation equations that result from Wentzel-Kramers-Brillouin theory. First, we establish that plane waves, which…

We prove that for a Wightman quantum field $\phi(x)$ the assumptions (i) positivity of the metric on the state space ${\cal H}$ of the theory (ii) the asymptotic condition in the form of Yang-Feldman equations and (iii) Klein-Gordon…

Starting from the von Neumann-Maxwell equations for the Wigner quasi-probability distribution and for the self-consistent electric field, the quantum analog of the classical single-wave model has been derived. The linear stability of the…

We discuss the dynamics of the quantum fluctuation around the nonlinear massive wave solution in the Higgs potential. In particular, we analyze the stability and instability of the mode function. Using the stability condition for Hill's…

Solving instability of Savvidy vacuum in QCD is a longstanding problem. Using light cone quantization we analyze the problem not in the real confining vacuum but in dense quark matter where gluons interact weakly with each other. We find a…

A new background field formulation of QCD is presented in which the background gluon field is not a classical field, but an operator made up of quantized quark fields. This background field allows colorless quark states to form exact…

A system of gluon fields generated at the earliest phase of relativistic heavy-ion collisions can be described in terms of classical fields. Numerical simulations show that the system is unstable but a character of the instability is not…

One possible solution of the cosmological constant problem involves a so-called $q$-field, which self-adjusts so as to give a vanishing gravitating vacuum energy density (cosmological constant) in equilibrium. We show that this $q$-field…

We consider the nonlinear wave equation, with a large exponent, power-like non-linearity, outside a ball of the Euclidean 3-dimensional space. In a previous article, we have proved that any global solution converges, up to a radiation term,…

We obtain the exact non-perturbative solution of a scalar field theory defined on a space with noncommuting position and momentum coordinates. The model describes non-locally interacting charged particles in a background magnetic field. It…

In this article, we study the standing-wave solutions to a class of systems of nonlinear Schr\"odinger equations. Our target is all the standard forms of the NLS systems, with two unknowns, that have a common linear part and cubic…

We consider the Cauchy problem for an energy supercritical nonlinear wave equation that arises in $(1+5)$--dimensional Yang--Mills theory. A certain self--similar solution $W_0$ of this model is conjectured to act as an attractor for…

Generalization of QCD motivated classical SU(2) Yang--Mills theory coupled to the scalar field is discussed. The massive scalar field, corresponding the scalar glueball, provides a confining potential for static, point-like, external…

The systematic approach to study bound states in quantum chromodynamics is presented. The method utilizes nonperturbative flow equations in the confining background, that makes possible to perform perturbative renormalization and to bring…

We consider the stability problem for standing waves of nonlinear Dirac models. Under a suitable definition of linear stability, and under some restriction on the spectrum, we prove at the same time orbital and asymptotic stability. We are…

We consider a massless, minimally coupled scalar with a quartic self-interaction which is released in Bunch-Davies vacuum in locally de Sitter background of an inflating universe. It was shown, in this system, that quantum effects can…

We consider the dynamics of the classical $SU(2)$ Wu-Yang monopole problem and show a set of new directions for its analysis starting from a variational setting. This allows us to give a new interpretation of the monopole charge as a string…