The Gell-Mann and Low switching allows to transform eigenstates of an unperturbed Hamiltonian H(0) into eigenstates of the modified Hamiltonian H(0) + V. This switching can be performed when the initial eigenstate is not degenerate, under some gap conditions with the remainder of the spectrum. We show here how to extend this approach to the case when the ground state of the unperturbed Hamiltonian is degenerate. More precisely, we prove that the switching procedure can still be performed when the initial states are eigenstates of the finite rank self-adjoint operator P(0)VP(0), where P(0) is the projection onto a degenerate eigenspace of H(0).

Gell-Mann and Low Formula for Degenerate Unperturbed States / C. h., Brouder; G., Stoltz; Panati, Gianluca. - In: ANNALES HENRI POINCARE'. - ISSN 1424-0637. - 10:7(2010), pp. 1285-1309. [10.1007/s00023-009-0018-7]

Gell-Mann and Low Formula for Degenerate Unperturbed States

PANATI, GIANLUCA
2010

Abstract

The Gell-Mann and Low switching allows to transform eigenstates of an unperturbed Hamiltonian H(0) into eigenstates of the modified Hamiltonian H(0) + V. This switching can be performed when the initial eigenstate is not degenerate, under some gap conditions with the remainder of the spectrum. We show here how to extend this approach to the case when the ground state of the unperturbed Hamiltonian is degenerate. More precisely, we prove that the switching procedure can still be performed when the initial states are eigenstates of the finite rank self-adjoint operator P(0)VP(0), where P(0) is the projection onto a degenerate eigenspace of H(0).
2010
01 Pubblicazione su rivista::01a Articolo in rivista
Gell-Mann and Low Formula for Degenerate Unperturbed States / C. h., Brouder; G., Stoltz; Panati, Gianluca. - In: ANNALES HENRI POINCARE'. - ISSN 1424-0637. - 10:7(2010), pp. 1285-1309. [10.1007/s00023-009-0018-7]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/143174
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