Analysis of the growth in complexity of a symmetry-invariant perturbation method for large N-body systems

The work required to solve for the fully interacting N boson wavefunction, which is widely believed to scale exponentially with N, has been previously shown to scale as N0 when the problem is rearranged using analytic building blocks. The exponential complexity reappears in an exponential scaling with the order of our perturbation series allowing exact analytical calculations for very large N systems through low order. In this paper, we analyse the growth in complexity with order when a normal mode basis is used.