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The Chern-Simons-like gravitational action is evaluated explicitly in four-dimensional space-time by radiative corrections at the one-loop level. The calculation is performed in the fermionic sector where the Dirac fermions interact with the background gravitational field, including the parity-violating term ψb/γ₅ψ. The investigation takes into account the weak field approximation and dimensional regularization scheme.
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Mariz et al. (2004) studied this question.
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