Microscopic Quantum Many-Body Theory

Introduction

Modern quantum many-body theory (QMBT) had its birth some 40 years ago, as a consequence of then recent developments in quantum field theory, particularly quantum electrodynamics. It has since then grown to become one of the most fundamental and exciting areas of modern theoretical physics. Its aims are both intellectually challenging and of fundamental and practical importance. Simply, stated ,they are to understand and predict the emergent properties of macroscopic matter that have their origins in the underlying interactions between the elementary constituents. By its very nature the subject is multidisciplinary. Actually, nearly all of physics is many-body physics at the most fundamental (i.e., the most microscopic) level of understanding appropriate to the energy scale of the particular branch of physics under discussion. There are fields like nuclear, atomic, molecular, and solid-state physics where the fundamentally many-particle aspects of the system under consideration are inmediatly apparent. For example, atomic nuclei, atoms, molecules, solids, and fluids are all manifestly interacting quantum many-body systems. There are other fields like elementary particle physics where it is less inmediately apparent that one is dealing with intrinsecally many-particle systems rather than only single or few particles. It is clear, however, that at one level of modeling, even such a "fundamental" particle as a neutron or proton may be wieved as as three quarks interacting via gluons. Thus, the single nucleon has itself become a multiparticle problem. From the above comments it should be clear that QMBT is not only an enormous subject in its own right, but also one that cuts across such areas as high-energy/particle physics, quantum field theory, nuclear physics, solid-state and condensed matter physics, statistical mechanics, electron and plasma physics, astrophysics, quantum chemistry, and materials science. Two aspects can be broadly distinguished in QMBT: the methods or techniques used to study a QMB system and the specific fields of applications. The methods range from the most fundamental and universal microscopic methods; as time independent perturbation theory, Green's function or propagator techniques, variational methods, the method of correlated basis functions, the coupled cluster method, to the more heuristic and phenomenological techniques as the Landau theory of Fermi liquids and the density functional theory. Finally, sitting as a paradigm between theory and experiment is the very important class of Monte Carlo or other stochastic simulation techniques, that have grown rapidly in importance in recent years due to the increasingly powerful computers. Obviously, the complexity of some systems precludes a direct application of QMBT in its standard forms. In those situations, the more heuristic or phenomelogical pictures seem to be more succesful in describing the experimental results or in suggesting new experiments. owever, this should be a challenge for microscopic theories beacuse finally is the microscopic description the only one that can give the complete picture of the problem. At present, the experimental situation in many fields , but specially in the field of condensed matter, is more in advance than its microscopic understanding and it is therefore necessary a theoretical effort to be able not only to describe and to understand the present experiments at the microscopic level but also to predict and suggest new experiments. Thus our goals are two-fold. One the one hand, we want to make use of the existing previous microscopic many-body theories to study increasingly reach and complex systems and problems, and on the other hand, largely driven by this objective, to develop new tools and algorithms to bring microscopic many-body theory to their fullest potential.

Nuclear Matter Phase Diagram