Algebraic Geometry of the Quark

Abstract

Using only the algebraic geometry defined by an irreducible representation of the Dirac ring we find an invariant tetrahedron that specifies the quadrupole shape occupied by nucleons with overwhelming probability, A simpler case is given by the cones occupied by spinning electrons. The Cayley cubic, which is invariant under the tetrahedral group, appears in Figure 2 and has 3 tangent cones representing quarks held together by an amorphous gluon condensate. This cubic is characterized by 9 lines emanating from the quarks and coincident with the edges of the tetrahedron. These quarks are short-lived because the representation is not time-invariant.

Keywords:

• P³
• Nuclear Quadrupoles
• Electron Spin Cones
• Quark Geometry
• Gluon Condensate
• Irreversibility