Projection operator approach to the self-energy
- Dipartimento di Fisica Nucleare e Teorica dell` Universita, Pavia and Istituto Nazionale di Fisica Nucleare, Sezione di Pavia (Italy)
- Institut de Physique B5, Universite de Liege, Sart Tilman, 4000 Liege 1 (Belgium)
Feshbach{close_quote}s projection operator formalism is extended to the description of the self-energy. This necessitates the introduction of {open_quote}{open_quote}extended{close_quote}{close_quote} projection operators. They act within an {open_quote}{open_quote}extended{close_quote}{close_quote} Hilbert space in which the number of nucleons is not fixed. The compact formula derived for the self-energy is formally similar to Feshbach{close_quote}s original expression of the {open_quote}{open_quote}generalized{close_quote}{close_quote} optical-model potential. The theory is formulated in the nuclear case, but it also applies to atomic systems. It covers both the {open_quote}{open_quote}retarded{close_quote}{close_quote} and the {open_quote}{open_quote}time-ordered{close_quote}{close_quote} Green{close_quote}s functions, and the {open_quote}{open_quote}proper{close_quote}{close_quote} and {open_quote}{open_quote}improper{close_quote}{close_quote} self-energies. It is first worked out in a stationary formalism, in order to better exhibit its analogy with Feshbach{close_quote}s original theory of the generalized optical-model potential. The main results are then also derived in a time-dependent framework. It is shown that, in finite systems, Dyson{close_quote}s equation does not uniquely determine the self-energy, in contrast to common assumption. However, the difference between the various possibilities has little practical consequence. We exhibit the relationship between the present approach and a recent {open_quote}{open_quote}configuration interaction formulation of the Dyson equation.{close_quote}{close_quote} Contact is also established with the {open_quote}{open_quote}linked-cluster{close_quote}{close_quote} perturbation expansion of the self-energy in powers of the strength of the nucleon{endash}nucleon interaction. Copyright {copyright} 1996 Academic Press, Inc.
- OSTI ID:
- 282099
- Journal Information:
- Annals of Physics (New York), Vol. 245, Issue 1; Other Information: PBD: Jan 1996
- Country of Publication:
- United States
- Language:
- English
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