arXiv subjects
Publications and source records attributed to Masao Hirokawa.
Regularities and higher order regularities of ground states of quantum field models are investigated through the fact that asymptotic annihilation operators vanish ground states. Moreover a sufficient condition for the absence of a ground state is given.
In the Nelson model particles interact through a scalar massless field. For hydrogen-like atoms there is a nucleus of infinite mass and charge $Ze$, $Z > 0$, fixed at the origin and an electron of mass $m$ and charge $e$. This system forms a bound state with binding energy $E_{\rm bin} = me^4Z^2/2$ to leading order in $e$. We investigate the radiative corrections to the binding energy and prove upper and lower bounds which imply that $ E_{\rm bin} = me^4 Z^2/2 + c_0 e^6 + \Ow(e^7 \ln e)$ with explicit coefficient $c_0$ and independent of the ultraviolet cutoff. $c_0$ can be computed by perturbation theory, which however is only formal since for the Nelson Hamiltonian the smallest eigenvalue sits exactly at the bottom of the continuous spectrum.
We consider a massless scalar Bose field interacting with two particles, one of them infinitely heavy. Neither an infrared nor an ultraviolet cutoff is imposed. In case the charge of the particles is of the same sign and sufficiently small, we prove the existence of a ground state.
We consider a two-dimensional electron with an anomalous magnetic moment, g>2, interacting with a nonzero magnetic field B perpendicular to the plane which gives rise to a flux F. Recent results about the discrete spectrum of the Pauli operator are extended to fields with the O(r^{-2-δ}) decay at infinity: we show that if |F| exceeds an integer N, there is at least N+1 bound states. Furthermore, we prove that weakly coupled bound states exist under mild regularity assumptions also in the zero flux case.