Title: The N-representability problem
Abstract: In quantum mechanics, "mixed" N-particle states are usually described in terms of N-particle density matrices. These matrices live in a high-dimensional space, can be reduced to matrices of much smaller dimension when taking into account the special form of the interactions between the particles in the system. Indeed, for calculating the energy of the system, it is sufficient to consider 2-particle density matrices when the system is described by 2-particle interactions. The problem of N-representability asks which 2-particle density matrices arise from an N-particle density matrix in this manner. This problem has been known since the 1950's but nobody has been able to solve it. In this talk, I will explain all the notions above in detail, present the problem, and the progress that has been done so far.