Abstract
The coupled cluster equations first proposed by Coester and Kümmel and developed by Kümmel, Lührmann, and Zabolitsky are derived explicitly from the variational principle for the ground state energy (the “true” energy) using a new set of simple formulas relating density matrices (equal time limits of Green functions) to the coupled cluster functions. In this respect a simplification appears to be achieved by working with a normalized ground state wave function. The further transformation of the variational equations into the standard forms given by the previous authors differs mainly in its pedagogical aspects from ideas found in the existing literature.
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References
For a thorough review of developments to 1977 see Kümmel, H., Lührmann, K.H., Zabolitsky, J.G.: Phys. Rep.36, 1 (1978). More recent developments may be traced from Refs. 2 and 3
The Many-Body Problem: Jastrow Correlations Versus Brueckner Theory. In: Lecture Notes in Physics. Guardiola, R., Ros, J. (eds.), Vol. 138. Berlin, Heidelberg, New York: Springer-Verlag 1981
Recent Progress in Many-Body Theories. In: Lecture Notes in Physics. Zabolitsky, J.G., Llano, M. de, Fortes, M., Clark, J.W. (eds.), Vol. 142. Berlin, Heidelberg, New York: Springer-Verlag 1981
Necessarily equivalent butdifferent expressions are quoted in Emrich, K., Zabolitsky, J.G., Lührmann, K.H.: Phys. Rev. C16, 1650 (1977), Eq. (4.16). Our quantities ℐn differ by a scale factor from theF n of Ref. 1 because we use anormalized state vector for the exact ground state. We emphasize that (1.5), which is our essential tool, appears nowhere in the work of Ref. 1, though we shall be able to derive it (trivially) by an algebraic completeness argument as well as by quoting results from the theory of diagrams, our initial approach. Expansions such as (1.5), in addition to their usefulness in a derivation of the equations of motion are also needed to calculate the averages of observables other than the energy
The quantities Φ n- correspond to the quantities called Σ n by Kümmel, H., Lührmann, K.H.: Nucl. Phys. A191, 525 (1972)
Lührmann, K.H.: Ann. Phys. (NY)103, 253 (1977). Arguments somewhat similar to those of this paper were developed by one of the authors (AK) in unpublished lecture notes (circa 1970)
Brandow, B.: Rev. Mod. Phys.39, 771 (1967)
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This work was supported in part by the U.S. Department of Energy under contract 40132-5-20441.