Related papers: Asymptotic behavior in the scalar field theory
We study the asymptotical behavior of the $p$-adic singular Fourier integrals $$ J_{\pi_{\alpha},m;\phi}(t) =\bigl< f_{\pi_{\alpha};m}(x)\chi_p(xt), \phi(x)\bigr> =F\big[f_{\pi_{\alpha};m}\phi\big](t), \quad |t|_p \to \infty, \quad t\in…
The effective potential for a scalar theory with $\lambda\phi^4$ interaction, coupled to a massless fermion through Yukawa interaction is calculated by summing over infinite number of two particle irreducible (2PI) diagrams of two different…
We discuss the lambda phi**4 model in 2- and 3-dimensional non-commutative spaces. The mapping onto a Hermitian matrix model enables its non-perturbative investigation by Monte Carlo simulations. The numerical results reveal a phase where…
We study the noncommutative \phi^4_4-quantum field theory at the self-duality point. This model is renormalisable to all orders as shown in earlier work of us and does not have a Landau ghost problem. Using the Ward identity of Disertori,…
We consider the perturbative treatment of the minimally coupled, massless, self-interacting scalar field in Euclidean de Sitter space. Generalizing work of Rajaraman, we obtain the dynamical mass m^2 \propto sqrt{lambda} H^2 of the scalar…
This paper explores cosmological scenarios in a scalar-tensor theory of gravity, including both a non-minimal coupling with scalar curvature of the form $R\phi^2$ and a non-minimal derivative coupling of the form…
We perform a detailed analysis on the dynamics of a Chiral-like cosmological model where the scalar fields can have negative kinetic terms. In particular, we study the asymptotic dynamics for the gravitational field equations for four…
Scalar fields appear in many theories beyond the Standard Model of particle physics. In the early universe, they are exposed to extreme conditions, including high temperature and rapid cosmic expansion. Understanding their behavior in this…
Asymptotic fields do not exist in theories with massless particles and fields, because the vacuum matrix elements of products of the interacting fields in such theories do not have delta function or principal value singularities in momentum…
We discuss the approach of effective field theory on a d-dimensional Euclidean space in a scalar theory with two different mass scales in the presence of flat surfaces. Then considering Dirichlet and Neumann boundary conditions, we…
We consider the repulsive Vlasov-Poisson system in dimension $d \geq 4$. A sufficient condition on the decay rate of the associated electric field is presented that guarantees the scattering and determination of the complete asymptotic…
A free massive scalar field in inhomogeneous random media is investigated. The coefficients of the Klein-Gordon equation are taken to be random functions of the spatial coordinates. The case of an annealed-like disordered medium, modeled by…
This paper presents the first examples of massless relativistic quantum field theories which are interacting and asymptotically complete. These two-dimensional theories are obtained by an application of a deformation procedure, introduced…
We study the asymptotic behaviour of the spectral gap of Schr\"odinger operators in two and higher dimensions and in a limit where the volume of the domain tends to infinity. Depending on properties of the underlying potential, we will find…
It is shown that in a $\lambda \phi^4$ theory of one real scalar field with spontaneous breaking of symmetry a calculation of the amplitudes of production by a virtual field $\phi$ of $n$ on-mass-shell bosons all being exactly at rest is…
We study two-to-two scattering amplitudes of a scalar particle of mass $m$. For simplicity, we assume the presence of $\mathbb{Z}_2$ symmetry and that the particle is $\mathbb{Z}_2$ odd. We consider two classes of amplitudes: the fully…
Probability distribution of non-Abelian parallel transporters on the group manifold and the corresponding amplitude are investigated for quantum Yang-Mills fields. It is shown that when the Wilson area law and the Casimir scaling hold for…
We apply the Hamiltonian formalism to investigate the massless sector of scalar field theory coupled with Maxwell electrodynamics through the Pontryagin term. Specifically, we analyze asymptotic symmetries at the null infinity of this…
We consider asymptotic behavior of the following fourth order equation \[ \Delta^2 u= \rho \frac{e^{u}}{\int_\Om e^{u} dx} {in} \Om, u= \partial_\nu u=0 {on} \partial \Omega \] where $\Om$ is a smooth oriented bounded domain in $\R^4$.…
The asymptotic behaviour of two classes of scalar field cosmological models are studied using the theory of dynamical systems: general relativistic Bianchi models containing matter and a scalar field with an exponential potential and a…