The lower part of the spectrum of the Hamiltonian of the spinless Pauli–Fierz model (A two-component Bose field interacting with a charged particle)

Minlos, R.

doi:10.1090/S0077-1554-08-00170-2

The lower part of the spectrum of the Hamiltonian of the spinless Pauli–Fierz model (A two-component Bose field interacting with a charged particle)
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by R. A. Minlos
Translated by: E. Khukhro

Trans. Moscow Math. Soc. 2008, 209-253

DOI: https://doi.org/10.1090/S0077-1554-08-00170-2

Published electronically: November 19, 2008

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Abstract:

We investigate a model of a vector massive spinless Bose field in the space $R^3$ interacting with a non-relativistic particle, where the interaction parameter is assumed to be sufficiently small. We study the ground state of the Hamiltonian $H_P$ for a fixed total momentum $P$ of the system and show that such a state is non-degenerate and exists only for a bounded domain of values of this momentum. We also show that, apart from the ground state, the operator $H_P$ has no other eigenvalues below the continuous spectrum. Furthermore, the next two, “one-boson”, branches of the spectrum of $H_P$ are constructed, which describe the scattering of one boson (with two possible polarization values) on the ground state.

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