Improved Approximations for Collective Neutrino Oscillations

A one- and two-body $\mathfrak{su}(n)$ Hamiltonian governing the dynamics of many systems, including collective neutrino oscillations, is investigated. We start by analyzing the algebraic structure($\mathfrak{u}(n^N)$), formulate a product structure of the algebra, and utilize this to construct generic expressions for operator expectation values, R\'{e}nyi Entropy, and Wigner Functions. Performing BBGKY hierarchy truncation we develop a systematic methodology for going beyond the mean field with polynomial scaling on a classical computer.