Massless Representations of the Poincaré Group

About the Book

Geometry through its fundamental transformations, the Poincaré 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.

About the Author

R. Mirman is the author of Group Theory: An Intuitive Approach, Group Theoretical Foundations of Quantum Mechanics, Massless Representations of the Poincaré Group: electromagnetism, gravitation, quantum mechanics, geometry, Point Groups, Space Groups, Crystals, Molecules, Quantum Mechanics, Quantum Field Theory: geometry, language, logic, and Quantum Field Theory, Conformal Group Theory, Conformal Field Theory: Mathematical and conceptual foundations, physical and geometrical applications.