I have a question about quantum perturbation in gravity. Is it necessary to express the divergent terms of loops as higher-order curvature terms like R_munuR^mun, etc.? Writing them as higher-order curvature terms implies that the corrections are incorporated through the dynamics of higher-order curvature terms at each step. As long as the loops are infinite, there will be an infinite number of higher-order curvature dynamics to combine. Can’t we directly reduce all the divergent terms recursively into lower-order derivative products of the metric tensor, such as (partial g_munu)(partial g^munu) and(partial g_munu)(partial g_rho sigma) g^mu rho g^nu sigma, etc.? This would shift the correction target to modifying the derivative terms of the metric tensor in the Lagrangian sqar(-g)(R+deltaR), where deltaR includes the corrected products of derivative metric tensors.
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I have a question about quantum perturbation in gravity. Is it necessary to express the divergent terms of loops as higher-order curvature terms like R_munuR^mun, etc.? Writing them as higher-order curvature terms implies that the corrections are incorporated through the dynamics of higher-order curvature terms at each step. As long as the loops are infinite, there will be an infinite number of higher-order curvature dynamics to combine. Can’t we directly reduce all the divergent terms recursively into lower-order derivative products of the metric tensor, such as (partial g_munu)(partial g^munu) and(partial g_munu)(partial g_rho sigma) g^mu rho g^nu sigma, etc.? This would shift the correction target to modifying the derivative terms of the metric tensor in the Lagrangian sqar(-g)(R+deltaR), where deltaR includes the corrected products of derivative metric tensors.
That's a great question. I haven't yet gone through this. I need to look into this, then only I can comment.
@ thank you