A gauge-invariant Wigner quantum mechanical theory is obtained by applying the Weyl-Stratonovich transform to von Neumann equation for density matrix. The reduces Weyl in electrostatic limit, when vector potential and thus magnetic field are zero. Both cases involve a center-of-mass followed Fourier integral on relative coordinate introducing momentum variable. latter continuous if limits of in...

Assume M is a compact oriented manifold of dimension at least 8. Moreover, let M be equipped with an equivariantly formal semi-free circle action, which has finite, nonempty fixed point set. We prove M has a perfect invariant MorseSmale function. The major ingredient in the proof is a new cancellation theorem for the invariant Morse theory.