Abstract
Abstract General relativity can be unambiguously formulated with Lorentz, de Sitter and anti-de Sitter tangent groups, which determine the fermionic representations. We show that besides of the Lorentz group only anti-de Sitter tangent group is consistent with all physical requirements.
Highlights
The existence of fermions forces us to consider the tangent group SO(3, 1), or equivalently the SL (2, C) group, in General Relativity
General relativity can be unambiguously formulated with Lorentz, de Sitter and anti-de Sitter tangent groups, which determine the fermionic representations
We show that besides of the Lorentz group only anti-de Sitter tangent group is consistent with all physical requirements
Summary
The existence of fermions forces us to consider the tangent group SO(3, 1), or equivalently the SL (2, C) group, in General Relativity. Abstract: General relativity can be unambiguously formulated with Lorentz, de Sitter and anti-de Sitter tangent groups, which determine the fermionic representations. Promoting the global Lorentz invariance of the Dirac action to a local one is achieved by introducing the spin-connection as the gauge field of the tangent group.
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