Abstract
We consider the quantization of matter fields in a background described by the teleparallel equivalent to general relativity. The presence of local Lorentz and gauge symmetries gives rise to different coupling prescriptions, which we analyse separately. As expected, quantum matter fields produce divergences that cannot be absorbed by terms in the background action of teleparallel equivalent to general relativity. Nonetheless, the formulation of teleparallel gravity allows one to find out the source of the problem. By imposing local Lorentz invariance after quantization, we show that a modified teleparallel gravity, in which the coefficients in the action are replaced by free parameters, can be renormalized at one-loop order without introducing higher-order terms. This precludes the appearance of ghosts in the theory.
Highlights
General relativity is one of the cornerstones of modern physics
By imposing local Lorentz invariance after quantization, we show that a modified teleparallel gravity, in which the coefficients in the action are replaced by free parameters, can be renormalized at one-loop order without introducing higher-order terms
We have studied the one-loop divergences produced by quantum fields coupled to a classical background described by teleparallel gravity
Summary
General relativity is one of the cornerstones of modern physics. It successfully describes the classical gravitational interaction in terms of the spacetime curvature, which results from the presence of matter. Despite all the differences with respect to general relativity, the dynamical equations of teleparallel gravity are equivalent to the Einstein field equations for a particular choice of the Lagrangian [see Eq (2.24)] This equivalence extends to the level of the action, where the boundary term in teleparallel gravity exactly reproduces the Gibbons– Hawking–York term [12]. A slight modification in the action of the gravitational sector can be performed in order to absorb all one-loop divergences from matter fields if one imposes local Lorentz symmetry after quantization (rather than before as usual) We stress that such a modification does not require higher derivatives, no ghosts or instabilities show up in the theory
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