Inserting the 3d momentum operator above and the energy operator into the 4-momentum (as a 1-form with (+ − − −) metric signature): P μ μ = ( E c , − − p ) obtains the 4-momentum operator : P ^ ^ μ μ = ( 1 c E ^ ^ , − − p ^ ^ ) = i ℏ ℏ ( 1 c ∂ ∂ ∂ ∂ t , ∇ ∇ ) = i ℏ ℏ ∂ ∂ μ μ where ∂ μ is the 4-gradient, and the − iħ becomes + iħ preceding the 3-momentum operator. This operator occurs in relativistic quantum field theory, such as the Dirac equation and other relativistic wave equations, since energy and momentum combine into the 4-momentum vector above, momentum and energy operators correspond to space and time derivatives, and they need to be first order partial derivatives for Lorentz covariance.