Massless Representations of the Poincaré Group: Electromagnetism, Gravitation, Quantum Mechanics, Geometry

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iUniverse, 2005 - Science - 236 pages
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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Contents

The Physical Meaning of Poincare Massless Representations
1
Massless Representations
12
Massless Fields are Different
32
How to Couple Massless and Massive Matter
56
The Behavior of Matter in Fields
73
Geometrical Reasons for the Poincare Group
95
Description of the Electromagnetic Field
123
The Equations Governing Free Gravitation
135
How Matter Determines Gravitational Fields
150
Nonlinearity and Geometry
165
Quantum Gravity
183
References
201
Index
207
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