The Coupled Cluster Method

Abstract

Liquids and solids, atoms and molecules, nuclei—all these clearly are interacting many‐body systems. Even a nucleon may be regarded as a manyparticle system, not just because it is now known to consist of three quarks interacting via gluons, but because of the possibility in quantum field theory of virtual excitation of many particles from the vacuum. in the table page 56 we list some of the many‐particle systems we encounter in the physical world at length scales that range from a few centimeters to a few fermis. Many of these systems exhibit phenomena—superconductivity in solids and fission in nuclei, for example—whose understanding does not follow immediately from knowledge of the constituents of the system and the interactions among the constituents, but requires new concepts and ideas. Many‐body physics is the branch of theoretical physics that studies the new phenomena or “emergent properties” that arise from interactions among “elementary” constituents of a many‐particle system and provides means and methods for carrying out precise calculations of such characteristic properties of these systems as may be compared with experimental results to verify hypotheses about the nature of the constituents and their interactions. Decomposing the wavefunction of a many‐particle system in terms of amplitudes for exciting clusters of a finite number of particles yields a versatile and high‐precision tool of many‐body theory.