Related papers: Klein-Gordon lower bound to the semirelativistic g…

In this paper we quantize the Klein--Gordon scalar field coupled to gravity in the instanton representation for spatially homogeneous variables. The construction provides a well-defined Hilbert space of states for generic self-interaction…

We prove the existence of ground states for the semi-relativistic Schr\"odinger-Poisson-Slater energy $$I^{\alpha,\beta}(\rho)=\inf_{\substack{u\in H^\frac 12(\R^3) \int_{\R^3}|u|^2 dx=\rho}} \frac{1}{2}\|u\|^2_{H^\frac 12(\R^3)}…

We study the {\it quasi-classical limit} of a quantum system composed of finitely many non-relativistic particles coupled to a quantized field in Nelson-type models. We prove that, as the field becomes classical and the corresponding…

Approximate analytical closed energy formulas for semirelativistic Hamiltonians of the form $\sigma\sqrt{\bm p^{2}+m^2}+V(r)$ are obtained within the framework of the auxiliary field method. This method, which is equivalent to the envelope…

A dynamically preferred quasi-local definition of gravitational energy is given in terms of the Hamiltonian of a `2+2' formulation of general relativity. The energy is well-defined for any compact orientable spatial 2-surface, and depends…

Consider an N-Boson system interacting via a two-body repulsive short-range potential $V$ in a three dimensional box $\Lambda$ of side length $L$. We take the limit $N, L \to \infty$ while keeping the density $\rho = N / L^3$ fixed and…

HVZ type theorem for semi-relativistic Pauli-Fierz Hamiltonian, $$\HHH=\sqrt{(p\otimes \one -A)^2+M^2}+V\otimes \one +\one\otimes \hf,\quad M\geq 0,$$ in quantum electrodynamics is studied. Here $H$ is a self-adjoint operator in Hilbert…

We review various attempts to localize the discrete spectra of semirelativistic Hamiltonians of the form H = \beta \sqrt{m^2 + p^2} + V(r) (w.l.o.g. in three spatial dimensions) as entering, for instance, in the spinless Salpeter equation.…

The Klein-Gordon equation in D-dimensions for a recently proposed Kratzer potential plus ring-shaped potential is solved analytically by means of the conventional Nikiforov-Uvarov method. The exact energy bound-states and the corresponding…

We propose nonlinear integral equations to describe the groundstate energy of the fractional supersymmetric sine-Gordon models. The equations encompass the N=1 supersymmetric sine-Gordon model as well as the phi_(id,id,adj) perturbation of…

We focus on the ground state of the cubic-quintic nonlinear Schr\"{o}dinger energy functional \begin{gather*} \begin{aligned} {E}(\varphi)=\frac{1}{2}\int_{\mathbb{R}^d}\left(|\nabla \varphi|^2+V(x)|\varphi|^2\right)\,dx…

We investigate existence and asymptotic completeness of the wave operators for nonlinear Klein-Gordon and Schr\"odinger equations with a defocusing exponential nonlinearity in two space dimensions. A certain threshold is defined based on…

We study the lowest energy E of a relativistic system of N identical bosons bound by pair potentials of the form V(r_{ij}) = g(r_{ij}^2) in three spatial dimensions. In natural units hbar = c = 1 the system has the semirelativistic…

We suppose: (1) that the ground-state eigenvalue E = F(v) of the Schroedinger Hamiltonian H = -Delta + vf(x) in one dimension is known for all values of the coupling v > 0; and (2) that the potential shape can be expressed in the form f(x)…

We show that the momentum, the density, and the electromagnetic field associated with the massive KleinGordon-Maxwell equations converge in the semi-classical limit towards their respective equivalents associated with the relativistic…

We present an extensive numerical study of the Sherrington-Kirkpatrick model in transverse field. Recent numerical studies of quantum spin-glasses have focused on exact diagonalization of the full Hamiltonian for small systems ($\approx$ 20…

We study interacting bosons on a three-dimensional Bravais lattice with positive hopping amplitudes and on-site repulsive interactions. We prove that, in the dilute limit $\rho\to 0$, the ground state energy density satisfies $$e_0(\rho) =…

With appropriate hypotheses on the nonlinearity $f$, we prove the existence of a ground state solution $u$ for the problem \[\sqrt{-\Delta+m^2}\, u+Vu=\left(W*F(u)\right)f(u)\ \ \text{in }\ \mathbb{R}^{N},\] where $V$ is a bounded…

Consider the focusing energy-critical Klein-Gordon equation in dimension d=3,4,5. We describe the global dynamics of real-valued solutions of which the energy is slightly larger than that of the ground states'. We classify the flows of the…

We consider a system of a quantum particle interacting with a quantum field and an external potential $V(\bx)$. The Hamiltonian is defined by a quadratic form $H^V = H^0 + V(\bx)$, where $H^0$ is a quadratic form which preserves the total…