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19S1 D. Anselmi
Theories of gravitation

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Book

D. Anselmi
From Physics To Life

A journey to the infinitesimally small and back

In English and Italian

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US: book | ebook  (in EN)
IT: book | ebook  (in IT)




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Archive for July 1994

We go on in the program of investigating the removal of divergences of a generical quantum gauge field theory, in the context of the Batalin-Vilkovisky formalism. We extend to open gauge-algebrae a recently formulated algorithm, based on redefinitions $\delta\lambda$ of the parameters $\lambda$ of the classical Lagrangian and canonical transformations, by generalizing a well-known conjecture on the form of the divergent terms. We also show that it is possible to reach a complete control on the effects of the subtraction algorithm on the space $M_{gf}$ of the gauge-fixing parameters. A principal fiber bundle $E \rightarrow M_{gf}$ with a connection $\omega_1$ is defined, such that the canonical transformations are gauge transformations for $\omega_1$. This provides an intuitive geometrical description of the fact the on shell physical amplitudes cannot depend on $M_{gf}$. A geometrical description of the effect of the subtraction algorithm on the space $M_{ph}$ of the physical parameters lambda is also proposed. At the end, the full subtraction algorithm can be described as a series of diffeomorphisms on $M_{ph}$, orthogonal to $M_{gf}$ (under which the action transforms as a scalar), and gauge transformations on $E$. In this geometrical context, a suitable concept of predictivity is formulated. We give some examples of (unphysical) toy models that satisfy this requirement, though being neither power counting renormalizable, nor finite.

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Class.Quant.Grav. 12 (1995) 319-350 | DOI: 10.1088/0264-9381/12/2/005

arXiv:hep-th/9407023

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Book

14B1 D. Anselmi
Renormalization

Course on renormalization, taught in 2015.

Last update: September 15th 2023, 242 pages

The final (2023) edition is vaibable on Amazon:

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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


The pdf file of the 2015 Edition is available here: PDF