Properties of the semiclassical functionals in the case of broken time reversal symmetry

Starting with a general one-body Hamiltonian which includes an <(alpha)over right arrow> . (p) over right arrow term describing the coupling between o rbital motion and the arbitrary vector field <(alpha)over right arrow>, we investigate some properties of the semiclassical functionals of various phy sical quantities. In particular, we show that these functionals could be wr itten in a very compact way. An approximate expression for the noninteracti ng total kinetic energy is given. We also show that these approximate semic lassical functionals transform by gauge transformation exactly as the corre sponding exact quantum functionals.