Dynamics of few-body states in a medium

Strongly interacting matter such as nuclear or quark matter leads to few-body bound states and correlations of the constituents. As a consequence quantum chromodynamics has a rich phase structure with spontaneous symmetry breaking, superconductivity, condensates of different kinds. All this appears in many astrophysical scenarios. Among them is the formation of hadrons during the early stage of the Universe, the structure of a neutron star, the formation of nuclei during a supernova explosion. Some of these extreme conditions can be simulated in heavy ion colliders. To treat such a hot and dense system we use the Green function formalism of many-body theory. It turns out that a systematic Dyson expansion of the Green functions leads to modified fewbody equations that are capable to describe phase transitions, condensates, cluster formation and more. These equations include self energy corrections and Pauli blocking. We apply this method to nonrelativistic and relativistic matter. The latter one is treated on the light front. Because of the medium and the inevitable truncation of space, the few-body dynamics and states depend on the thermodynamic parameters of the medium. Many-body Green functions. To treat hot and dense quantum systems, such as nuclear or quark matter in question here, we use the techniques of many-body Green functions [1]. We organize the Green functions into a Dyson expansion that leads to a hierarchy of linked cluster equations [2]. In recent years we have systematically applied this approach for finite temperatures up to multi-nucleon clusters (see e.g. [3] and refs therein) and also generalized it to light front dynamics [4, 5]. In fact, the light front quantization is well suited to use the many-body Green function formalism as in the relativistic case, as it utilizes the Fock space expansion [6]. We define a chronological Green function