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

We study a new generating functional of one-particle irreducible diagrams in quantum field theory, called master functional, which is invariant under the most general perturbative changes of field variables. The functional $\Gamma$ does not transform as a scalar under the transformation law inherited from its very definition, although it does transform as a scalar under an unusual transformation law. The master functional, on the other hand, is the Legendre transform of an improved functional W = ln Z with respect to the sources coupled to both elementary and composite fields. The inclusion of certain improvement terms in W and Z is necessary to make this transform well defined. The master functional behaves as a scalar under the transformation law inherited from its very definition. Moreover, it admits a proper formulation, obtained extending the set of integrated fields to the so-called proper fields, which allows us to work without passing through Z, W or $\Gamma$. In the proper formulation the classical action coincides with the classical limit of the master functional, and correlation functions and renormalization are calculated applying the usual diagrammatic rules to the proper fields. Finally, the most general change of field variables, including the map relating bare and renormalized fields, is a linear redefinition of the proper fields.

PDF

Eur. Phys. J. C 73 (2013) 2385 | DOI: 10.1140/epjc/s10052-013-2385-y

arXiv:1205.3584 [hep-th]

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Book

14B1 D. Anselmi
Renormalization

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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.)