19R1 D. Anselmi
Theories of gravitation



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Archive for September 2005

The infinite reduction of couplings is a tool to consistently renormalize a wide class of non-renormalizable theories with a reduced, eventually finite, set of independent couplings, and classify the non-renormalizable interactions. Several properties of the reduction of couplings, both in renormalizable and non-renormalizable theories, can be better appreciated working at the regularized level, using the dimensional-regularization technique. We show that, when suitable invertibility conditions are fulfilled, the reduction follows uniquely from the requirement that both the bare and renormalized reduction relations be analytic in $\varepsilon=D-d$, where $D$ and $d$ are the physical and continued spacetime dimensions, respectively. In practice, physically independent interactions are distinguished by relatively non-integer powers of epsilon. We discuss the main physical and mathematical properties of this criterion for the reduction and compare it with other equivalent criteria. The leading-log approximation is solved explicitly and contains sufficient information for the existence and uniqueness of the reduction to all orders.


J.High Energy Phys. 01 (2006) 077 | DOI: 10.1088/1126-6708/2006/01/077

arXiv: hep-th/0509196


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.)

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