The Hamiltonian analysis for the linearized λ R gravity plus a Chern-Simons term is performed. The first-class and second-class constraints for arbitrary values of λ are presented, and one physical degree of freedom is reported. The second-class constraints are removed, and the corresponding generalized Dirac brackets are constructed; then, the difference between theories with different values of λ is remarked.
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Escalante et al. (2024) studied this question.
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