Abstract
In this paper we discuss the limiting absorption principle (l.a.p.) of the second quantization of semi-bounded self-adjoint operators. We show that the l.a.p. for a self-adjoint operator on a basic Hilbert space $\mathcal{H}$ is ``inherited'' to the one for its second quantization on a Fock space $\mathcal{F}(\mathcal{H})$. In order to show such a result, we examine the resolvent of $n$-body problem and take the limit of the infinite direct sum of those operators in a suitable subspace of $\mathcal{F}(\mathcal{H})$.
Citation
Shoji SHIMIZU. "Limiting absorption principle for the second quantization of self-adjoint operators." Hokkaido Math. J. 39 (2) 239 - 259, May 2010. https://doi.org/10.14492/hokmj/1277385663
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