Recent theorems

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Poles


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 other non-dominant quadratic terms as “two-leg vertices”.

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14B1 D. Anselmi
Renormalization

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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.)