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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 1998-32
December 1998

Spectral and scattering theory of spatially cut-off $P(varphi)_{2}$ Hamiltonians


J. Derezinski, C. Gérard


We study spatially cut-off $P(varphi)_2$ Hamiltonians. We show the local finiteness of the pure point spectrum outside of thresholds, the limiting absorption principle and asymptotic completeness of scattering for such Hamiltonians. Our results imply the absence of singular continuous spectrum.

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This paper has now been published in Commun. Math. Phys. 213, 39-125 (2000)