Abstract
The manifestly covariant canonical formalism of quantum gravity is extended to a coupled system of quantum gravity and a non-abelian gauge field in the Suzuki gauge, where the Suzuki gauge is a special gauge fixing in which the part corresponding to the Cartan subalgebra behaves like an abelian gauge theory. An indecomposable superalgebra is found which unifies the spacetime symmetry and the Cartan subalgebra without contradicting the no-go theorem.
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