The above case is of the most physical interest. We view R n as Minkowski spacetime. Since the gauge group of electromagnetism is U ( 1 ) , connection 1-forms for L are nothing more than the valid electromagnetic four-potentials on R n . If F = d A is the electromagnetic tensor, then the massless Maxwell – Klein–Gordon system for a section ϕ ϕ of L are { ∂ ∂ μ μ F μ μ ν ν = Im ⁡ ⁡ ( ϕ ϕ D ν ν ϕ ϕ ) D μ μ D μ μ ϕ ϕ = 0 and the energy of this physical system is | | F ( t ) | | L x 2 2 2 + | | D ϕ ϕ ( t ) | | L x 2 2 2 . The diamagnetic inequality guarantees that the energy is minimized in the absence of electromagnetism, thus A = 0 .