Abstract
In a perturbative approach Einstein-Hilbert gravity is quantized about a flat background. In order to render the model power counting renormalizable, higher order curvature terms are added to the action. They serve as Pauli-Villars type regulators and require an expansion in the number of fields in addition to the standard expansion in the number of loops. Renormalization is then performed within the BPHZL scheme, which provides the action principle to construct the Slavnov-Taylor identity and invariant differential operators. The final physical state space of the Einstein-Hilbert theory is realized via the quartet mechanism of Kugo and Ojima. Renormalization group and Callan-Symanzik equation are derived for the Green functions and, formally, also for the $S$-matrix.
Highlights
In the perturbative construction of Einstein-Hilbert (EH) gravity on four-dimensional spacetime one splits the metric gμν into a background gμν and oscillations hμν around it which are quantized
Suppose we would like to gauge the translations in a matter model, say a massless scalar field of canonical dimension one, with the usual Noether procedure, one lets the parameter aμ of the translations depend on x and couples the respective conserved current, the energymomentum-tensor Tμν (EMT), to an external tensor field hμν
In the present paper we propose the perturbative quantization of classical Einstein-Hilbert gravity
Summary
In the perturbative construction of Einstein-Hilbert (EH) gravity on four-dimensional spacetime one splits the metric gμν into a background gμν and oscillations hμν around it which are quantized. Suppose we would like to gauge the translations in a matter model, say a massless scalar field of canonical dimension one, with the usual Noether procedure, one lets the parameter aμ of the translations depend on x and couples the respective conserved current, the energymomentum-tensor Tμν (EMT), to an external tensor field hμν This entails the field h with transformations dictated by the local translations. The main gain of this version to deal with the UV infinities is that one has an action principle [12] at one’s disposal which one would not have in the power counting nonrenormalizable EH model The hurdle that this scheme is not BRST invariant can be overcome by cohomology results existing in the literature since the 1980s (see [13]).
Sign-in/Register to view highlights & summary 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 callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
