From Random Walks to Random Matrices

1: The random walk: universality and continuum limit
2: Functional integration: from path to field integrals
3: The essential role of functional integrals in modern physics
4: From infinites in QED to the general renormalization group
5: Renormalization group: From a general concept to numbers
6: Critical phenomena: the field theory approach
7: Stability of RG fixed points and decay of correlations
8: Quantum field theory: an effective theory
9: The non-perturbative renormalization group
10: O(N) vector model in the ordered phase: Goldstone modes
11: Gauge invariance and gaude fixing
12: The discovery of the Higgs boson: a major achievement and a problem
13: Quantum Chromodynamics (QCD): A non-Abelian gauge theory
14: Non-Abelian gauge theories: renormalization and Zinn-Justin equation
15: Quantum field theory: asymptotic safety
16: Symmetries: from classical to quantum field theories
17: Quantum anomalies: A few physics applications
18: Periodic semi-classical vacuum, instantons and anomalies
19: Field theory in a finite geometry: finite size scaling
20: The weakly interacting Bose gas at the critical temperature
21: Quantum field theory at finite temperature
22: From random walk to critical dynamics
23: Field theory: Peturbative expansion and summation methods
24: Hyper-asymptotic expansions and instantons
25: Renormalization group approach to matric models

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• A física quântica (mecânica quântica e teoria quântica de campos)
• Física das partículas e da energia elevada
• Física Matemática