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Mathematical Aspects of Quantum Field Theory and String Theory


Introduction to Topological Field Theory


  • Localization formulae and equivariant cohomology
  • Supersymmetric Quantum Mechanics and Morse theory
  • Supersymmetric sigma-models and topological twist
  • A and B models, quantum cohomology and mirror symmetry

Geometry of Gauge Fields


1.The electromagnetic feld

Facts from Physics: a) Electrostatics, b) Magnetostatics, c) Electromagnetism.

Differential forms on R^n. Potentials, gauge invariance and wave equation.

4-dimensional form of Maxwell equations.

2.Matter and gauge fields

Space-time.Spinors. Action functionals for matter fields.

Noether's theorem and conservation laws.


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