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Few-body correlations and their role in many-body physics


This project is comprised of the study of few-body correlations and their role in many-body systems in the areas of fundamental, nuclear, hadronic and atomic physics. Its aim is to provide continuity to the research performed in these areas by the principal investigators, in their several collaborations. The team of principal investigators (Brett Vern Carlson, Tobias Frederico, and Lauro Tomia), have a long history of collaborations between themselves, which has started more than 10 years ago, within the main lines of research proposed in this tematic, as one can observe in the details of the project. We divide the project in five basic directions of study. Universal aspects of few-body systems and hamiltonian renormalization. Few-body correlations in the nuclear medium. Few-body correlations in the phenomenology of hadrons. Few-body correlations in atomic and molecular condensates. Computational methods. The structure of few-body correlations, in the vacuum as well as at finite densities, have been extensively studied by the principal investigators of this thematic group, through collaborations among themselves and with other researchers. Throughout these collaborations, which were initially in the area of low-energy nuclear physics, the research developed by the investigators evolved into a study of few-body correlations in a wider physical con-text, from particle physics to atomic and molecular physics. Of special interest in all of these studies are the computational methods developed in the early phase, in the con-text of low-energy nuclear physics, which were later adapted to the study of few-body correlations at high energies (relativistic particle and nuclear physics) and at typical low energies, such as those of atomic condensates. Under the topic universal aspects of few-body systems and Hamiltonian renormalization, we will study the generalization of correlations between observables in few-body systems in nuclear and atomic/molecular physics that constrain the physical information brought by few-body correlations to the many body system. From a formal point of view, the concept of a fixed-point Hamiltonian will be applied to the Hamiltonian renormalization of interacting N-body quantum systems through a two-body potential containing a Dirac-delta singularity and its derivatives, characterized by the effective expansion of the two-body interaction. The renormalized and regularized equations for the T-matrix, given by subtracted equations, can be derived from a Hamiltonian containing the counter terms necessary to make the integral equations well defined…(AU)

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