Let p : L → → R n be a U(1) line bundle, and let A be a connection 1-form for L . In this situation, A is real-valued, and the covariant derivative D satisfies D f j = ( ∂ ∂ j + i A j ) f for every section f . Here ∂ ∂ j are the components of the trivial connection for L . If A j ∈ ∈ L loc 2 ( R n ) and f , ( ∂ ∂ 1 + i A 1 ) f , … … , ( ∂ ∂ n + i A n ) f ∈ ∈ L 2 ( R n ) , then for almost every x ∈ ∈ R n , it follows from the diamagnetic inequality that | ∇ ∇ | f | ( x ) | ≤ ≤ | D f ( x ) | .