Abstract
We give a simple proof of perturbative unitarity in gauge theories and quantum gravity using a special gauge that allows us to separate the physical poles of the free propagators, which are quantized by means of the Feynman prescription, from the poles that belong to the gauge-trivial sector, which are quantized by means of the fakeon prescription. The proof applies to renormalizable theories, including the ultraviolet complete theory of quantum gravity with fakeons formulated recently, as well as low-energy (nonrenormalizable) theories. We clarify a number of subtleties related to the study of scattering processes in the presence of a cosmological constant Λ. The scattering ampli- tudes, defined by expanding the metric around flat space, obey the optical theorem up to corrections due to Λ, which are negligible for all practical purposes. Problems of interpretation would arise if such corrections became important. In passing, we obtain local, unitary (and “almost” renormalizable) theories of massive gravitons and gauge fields, which violate gauge invariance and general covariance explicitly.
Highlights
We give a simple proof of perturbative unitarity in gauge theories and quantum gravity using a special gauge that allows us to separate the physical poles of the free propagators, which are quantized by means of the Feynman prescription, from the poles that belong to the gauge-trivial sector, which are quantized by means of the fakeon prescription
The Euclidean diagram), but they are bypassed in different ways: (ii-a) the thresholds associated with the processes that involve at least one fakeon are circumvented by means of the average continuation [8, 11, 12], which is the arithmetic average of the two analytic continuations; (ii-b) instead, the physical thresholds are circumvented analytically, as usual
We use the λ dependence inside the loop diagrams to distinguish the physical thresholds, which are overcome analytically, from the fake thresholds, which are overcome by means of the average continuation
Summary
We prove unitarity in Abelian and non-Abelian gauge theories in dimensions d > 2, by quantizing the gauge-trivial sector with the fakeon prescription. The second term describes the violation of gauge invariance at nonvanishing gauge masses mg and disappears in the limit mg → 0 Lorentz invariance is broken by the quantization prescription (2.3) It is recovered in the limit of vanishing gauge masses. By means of the fakeon quantization prescription, it is possible to build local, unitary, strictly renormalizable Yang-Mills theories in arbitrary higher spacetime dimensions d 6 [27, 28]. The proof of unitarity proceeds as above, as well as the recovery of gauge invariance and Lorentz invariance at vanishing gauge masses
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
