02-498 Fumio Hiroshima

Photon number localization of ground states in nonrelativistic QED (80K, latex) Nov 30, 02

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Abstract. One electron system minimally coupled to a quantized radiation field is considered. It is assumed that the quantized radiation field is {\it massless}, and {\it no} infrared cutoff is imposed. The Hamiltonian, $H$, of this system is defined as a self-adjoint operator acting on $\LR\otimes\fff$, where $\fff$ is the Boson Fock space over $L^2(\BR\times\{1,2\})$. It is shown that the ground state, $\gr$, of $H$ belongs to $\cap_{k=1}^\infty D(1\otimes N^k)$, where $N$ denotes the photon number operator of $\fff$. Moreover it is shown that, for almost every electron position variable $x\in\BR$ and for arbitrary $k\geq 0$, $\|(1\otimes \N)\gr (x) \|_\fff \leq D_ke^{-\delta |x|^{m+1}}$ with some constants $m$, $D_k$, and $\delta$ independent of $k$. In particular $\gr\in \cap_{k=1}^\infty D (e^{\beta |x|^{m+1}}\otimes N^k)$ for $0<\beta<\delta/2$ is obtained.

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