given above. Taking Φ Φ = C , the function ϕ ϕ : M → → C can be interpreted as a wave function, and its Laplacian the kinetic energy of that wave function. The ⟨ ⟨ ⟨ ⟨ ⋅ ⋅ , ⋅ ⋅ ⟩ ⟩ ⟩ ⟩ is just some geometric machinery reminding one to integrate over all space. The corresponding quantum mechanical notation is ϕ ϕ = | ψ ψ ⟩ ⟩ . In flat space, the Laplacian is conventionally written as Δ Δ = ∇ ∇ 2 . Assembling all these pieces together, the sigma model action is equivalent to