Course

19R1 D. Anselmi
Theories of gravitation

Last update: October 5th 2018

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

To be held in the first part of 2019 – Stay tuned

Program

Recent Papers

Renormalization-group flow

The trace anomaly in external gravity is the sum of three terms at criticality: the square of the Weyl tensor, the Euler density and $\Box R$, with coefficients, properly normalized, called $c$, $a$ and $a’$, the latter being ambiguously defined by an additive constant. Considerations about unitarity and positivity properties of the induced actions allow us to show that the total RG flows of $a$ and $a’$ are equal and therefore the $a’$-ambiguity can be consistently removed through the identification $a’=a$. The picture that emerges clarifies several long-standing issues. The interplay between unitarity and renormalization implies that the flux of the renormalization group is irreversible. A monotonically decreasing $a$-function interpolating between the appropriate values is naturally provided by $a’$. The total $a$-flow is expressed non-perturbatively as the invariant (i.e. scheme-independent) area of the graph of the beta function between the fixed points. We test this prediction to the fourth loop order in perturbation theory, in QCD with $N_f \lesssim 11/2 N_c$ and in supersymmetric QCD. There is agreement also in the absence of an interacting fixed point (QED and $\phi^4$-theory). Arguments for the positivity of $a$ are also discussed.

PDF

Annals Phys. 276 (1999) 361-390 | DOI: 10.1006/aphy.1999.5949

arXiv:hep-th/9903059

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Book

14B1 D. Anselmi
Renormalization

Read in flash format

PDF

Last update: May 9th 2015, 230 pages

Contents:
Preface
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
References

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