19R1 D. Anselmi
Theories of gravitation

Last update: October 5th 2018

PhD course – 54 hours – Videos of lectures and PDF files of slides

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Recent Papers

We prove the renormalizability of various theories of classical gravity coupled with interacting quantum fields. The models contain vertices with dimensionality greater than four, a finite number of matter operators and a finite or reduced number of independent couplings. An interesting class of models is obtained from ordinary power-counting renormalizable theories, letting the couplings depend on the scalar curvature R of spacetime. The divergences are removed without introducing higher-derivative kinetic terms in the gravitational sector. The metric tensor has a non-trivial running, even if it is not quantized. The results are proved applying a certain map that converts classical instabilities, due to higher derivatives, into classical violations of causality, whose effects become observable at sufficiently high energies. We study acausal Einstein-Yang-Mills theory with an R-dependent gauge coupling in detail. We derive all-order formulas for the beta functions of the dimensionality-six gravitational vertices induced by renormalization. Such beta functions are related to the trace-anomaly coefficients of the matter subsector.


Class. Quant. Grav. 24 (2007) 1927 | DOI:  10.1088/0264-9381/24/8/003

arXiv: hep-th/0611131

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14B1 D. Anselmi

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Last update: May 9th 2015, 230 pages

1. Functional integral
2. Renormalization
3. Renormalization group
4. Gauge symmetry
5. Canonical formalism
6. Quantum electrodynamics
7. Non-Abelian gauge field theories
Notation and useful formulas

Course on renormalization, taught in Pisa in 2015. (More chapters will be added later.)