College of Liberal Arts & Sciences

# Math Physics Seminar

**Abstract:**

The projective symmetry of the geodesic equation, related to diffeomorphism invariance, expresses the equivalence among connections describing the same geodesic path. This symmetry is applied to the massless Dirac action and the associated gauge field with chiral coupling is identified. The electroweak and Higgs sectors of the Standard Model are then considered under this symmetry and it is shown to effect the forms of the boson masses and the Higgs potential with an energy scale dependence. It is also shown that this symmetry is "`dark" with respect to the fermions of the electroweak model. Projective symmetry is then used in tandem with the seesaw mechanism to provide almost-chiral masses for left and right handed neutrinos, which is shown to possibly contain an oscillatory rescaling of the Yukawa coupling of neutrinos to the Higgs.