Massless Representations of the Poincare Group Electromagnetism, Gravitation, Quantum Mechanics, Geometry

Geometry through its fundamental transformations, the Poincare group, requires that wavefunctions belong to representations. Massless and massive representations are very different and their coupling almost impossible. Helicity-1 gives electromagnetism, helicity-2 gives gravitation; no higher helicities are possible. Basis states, thus the fundamental fields, are the potential and connection. General relativity is derived and is the unique theory of gravity, thus the only possible quantum theory of gravity. It is explained why it is. Because of transformations trajectories must be geodesics. Momenta are covariant derivatives and must commute. Covariant derivatives of the metric are zero.Mirman, R. is the author of 'Massless Representations of the Poincare Group Electromagnetism, Gravitation, Quantum Mechanics, Geometry', published 2005 under ISBN 9780595341245 and ISBN 0595341241.