Discrete Symmetry, Toral Symmetry and the Euler Characteristic of Manifolds

Discrete Lorentz symmetry and discrete time translational symmetry

The Lorentz symmetry and the space and time translational symmetry are fundamental symmetries of nature. Crystals are themanifestation of the continuous space translational symmetry being spontaneously broken into a discrete one.We argue that, following the space translational symmetry, the continuous Lorentz symmetry should also be broken into a discrete one, which further implies that the con...

Symmetry of Fullerene C_60

Discrete Lorentz symmetry and discrete time translational symmetry

The Lorentz symmetry and the space and time translational symmetry are fundamental symmetries of nature. Crystals are themanifestation of the continuous space translational symmetry being spontaneously broken into a discrete one.We argue that, following the space translational symmetry, the continuous Lorentz symmetry should also be broken into a discrete one, which further implies that the con...

Mirror Symmetry and Fano Manifolds

Gravity and Discrete Symmetry

Using the differential calculus on discrete group, we study the general relativity in the space-time which is the product of a four dimensional manifold by a two-point space. We generalize the usual concept of frame and connection in our space-time, and from the generalized torsion free condition we obtain an action of a scalar field coupled to Einstein gravity, which may be related to the Jord...