Course

19S1 D. Anselmi
Theories of gravitation

Program

PDF

Book

D. Anselmi
From Physics To Life

A journey to the infinitesimally small and back

In English and Italian

Available on Amazon:
US: book | ebook  (in EN)
IT: book | ebook  (in IT)




Recent Papers




13T1 Theorem
Replacing fields with the solutions of their field equations preserves the master equation


Let $S(\Phi,U,K,K_{U})$ denote the solution of the master equation $(S,S)=0$, where $\{\Phi ^{A},U\}$ are the fields and $\{K_{A},K_{U}\}$ are the sources coupled to the $\Phi ^{A}$- and $U$-gauge transformations. If we replace $U$ with the solution $U^{*}(\Phi ,K,K_{U})$ of the $U$-field equations
\begin{equation}
\frac{\delta _{r}S}{\delta U}=0,
\end{equation} read more


12T1 Theorem
Procedure to convert the functional integral to the conventional form


Consider a functional integral
\[
\mathcal{I}=\int [\mathrm{d}\varphi ]\hspace{0.02in}\exp \left( -S(\varphi)+\int J\left( \varphi -bU\right) \right) ,
\]
where $U(\varphi ,bJ)$ is a local function of $\varphi$ and $J$, and $b$ is a constant. Then there exists a perturbatively local change of variables
\[
\varphi =\varphi (\varphi ^{\prime },b,bJ)=\varphi... read more


06T1 Theorem
Terms quadratically proportional to the field equations and field redefinitions


Consider an action $S$ depending on fields $\phi_{i}$, where the index $i$ labels both the field type, the component and the spacetime point. Add a term quadratically proportional to the field equations $S_{i}\equiv \delta S/\delta \phi _{i}$ and define the modified action
\begin{equation}
\phantom{(1)}\qquad\qquad\qquad S^{\prime }(\phi _{i})=S(\phi _{i})+S_{i}F_{ij}S_{j},... read more


05T1 Theorem
Maximum poles of Feynman diagrams


The maximum pole of a diagram with $V$ vertices and $L$ loops is at most $1/\varepsilon^{m(V,L)}$, where $m(V,L)=\min (V-1,L).$ The result holds in dimensional regularization, where $\varepsilon = d-D$, $d$ is the physical dimension and $D$ the continued one. Moreover, vertices are counted treating mass terms and the... read more


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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:

US  IT  DE  FR  ES  UK  JP  CA


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