Running couplings from adiabatic regularization

Abstract

We extend the adiabatic regularization method by introducing an arbitrary mass scale $\mu$ in the construction of the subtraction terms. This allows us to obtain, in a very robust way, the running of the coupling constants by demanding $\mu$-invariance of the effective semiclassical (Maxwell-Einstein) equations. In particular, we get the running of the electric charge of perturbative quantum electrodynamics. Furthermore, the method brings about a renormalization of the cosmological constant and the Newtonian gravitational constant. The running obtained for these dimensionful coupling constants has new relevant (non-logarithmic) contributions, not predicted by dimensional regularization.

Revised version. Some points clarified. New references added. 6 pages. To appear in Phys. Lett. B

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• Adiabatic regularization for Dirac fields in time-varying electric backgrounds
• Hadamard renormalization for a charged scalar field
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• Running gravitational couplings, decoupling, and curved spacetime renormalization
• R-summed form of adiabatic expansions in curved spacetime
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• Ultraviolet-regularized power spectrum without infrared distortions in cosmological spacetimes
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• Induced energy-momentum tensor of Dirac field in 2D de Sitter QED
• Physical scale adiabatic regularization in cosmological spacetimes