Massless Representations of the Poincaré Group: Electromagnetism, Gravitation, Quantum Mechanics, Geometry
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.
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The Physical Meaning of Poincare Massless Representations
Massless Fields are Different
How to Couple Massless and Massive Matter
The Behavior of Matter in Fields
Geometrical Reasons for the Poincare Group
Description of the Electromagnetic Field
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angular momentum basis vectors Bianchi identity charge classical commutation relations components connection consider constant coupling covariant derivative curvature curved defined depend described determined diagonal Dirac equation effect eigenstates eigenvalues Einstein's equation electromagnetic field electron energy-momentum tensor Euclidean expectation value experimental flat space free gravitation fundamental gauge transformations geodesic geometry give given gravitational field gravitational statefunction gravitational wave gravitons group theory Hamiltonian helicity inhomogeneous group JV's linear representations little group Lorentz group Lorentz subgroup mass massive objects massless objects massless representations mathematical matrices matter Mirman momenta nonlinear representation nonzero observers ordinary derivative parameters phase photon physical objects Poincare algebra Poincare basis Poincare group Poincare invariance Poincare representation Poincare transformations properties quantum mechanics quantum theory realization representation class rotation group scalar semisimple groups solutions space-dependent spin spinor statefunction symmetric theory of gravitation three-indexed tions translations vector potential wavepacket zero zero-mass zero-momentum