which is just the grand-total kinetic energy of the wave-function ψ ψ ( x ) , up to a factor of ℏ ℏ / m . To conclude, the classical sigma model on C can be interpreted as the quantum mechanics of a free, non-interacting quantum particle. Obviously, adding a term of V ( ϕ ϕ ) to the Lagrangian results in the quantum mechanics of a wave-function in a potential. Taking Φ Φ = C n is not enough to describe the n -particle system, in that n particles require n distinct coordinates, which are not provided by the base manifold. This can be solved by taking n copies of the base manifold.