Quantum Many-Body Systems

To date, one of the major challenges confronting physicists is associated with the strongly correlated or strongly interacting many-body systems. When particles interact weakly, the physics of the quantum many-body systems can be systematically studied via the Feynman diagram perturbation expansion technique. However, for strongly interacting many-body systems, there is no systematical non-perturbative approach developed. To this end, it is interesting to note that the coherent state representation can provide a natural framework for a non-perturbation treatment to the many-body physics, and in particular, the Hartree-Fock or Hartree-Fock-Bogoliubov transformations can easily and systematically be realized. In fact, the coherent states can generate all kinds of low-energy excitations of many-body systems, such as superconductivity, superfluity, and other low-energy excitations. These form the keys to understand the emergence of complexities of many-body dynamics.