Studies

201
Compulsory

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I. Historical overview:

The development of elementary particle physics and Quantum field theory

II. Scalar Fields

  • Classical field theory, Noether theory, equations of motion
  • Canonical quantization of the scalar field
  • The neutral free scalar field
  • The charged free scalar field
  • Particle Green's functions
  • Interacting fields and particle scattering
  • Path-integral formalism
  • Feynman rules
  • Scattering cross sections for scalar particle

III. Particles with spin

  • Fermions: Relativistic theory (Pauli, Dirac, Weyl equations, Dirac matrices, phase symmetry)
  • Abelian gauge symmetry and vector fields: Photon
  • Canonical quantization of the Dirac field
  • Path integral for fermion fields, Grassmann variables, Feynman rules
  • Proca field; helicity states
  • Quantization of Abelian vector fields and quantum electrodynamics
  • Non-Abelian gauge theories: Yang-Mills fields
  • Faddeev-Popov ghosts
  • Slavnov-Taylor identities
  • Feynman rules for Yang-Mills fields
  • Perturbation theory

IV Renormalization of quantum field theories

  • Renormalizable and non-renormalizable field theories
  • Loop integrals and regularization in D dimensions
  • Renormalization in quantum electrodynamics
  • Dyson-Ward proof
  • Path integrals, Ward-Takahashi Identity
  • Becchi-Rouet-Stora transformation
  • Bogolyubov-Parasyuk-Hepp-Zimmermann renormalization proof of the quantum field theories
  • The renormalization group: Callan-Symanzik equations, running couplings and masses
I. Historical overview:

The development of elementary particle physics and Quantum field theory

II. Scalar Fields

  • Classical field theory, Noether theory, equations of motion
  • Canonical quantization of the scalar field
  • The neutral free scalar field
  • The charged free scalar field
  • Particle Green's functions
  • Interacting fields and particle scattering
  • Path-integral formalism
  • Feynman rules
  • Scattering cross sections for scalar particle

III. Particles with spin

  • Fermions: Relativistic theory (Pauli, Dirac, Weyl equations, Dirac matrices, phase symmetry)
  • Abelian gauge symmetry and vector fields: Photon
  • Canonical quantization of the Dirac field
  • Path integral for fermion fields, Grassmann variables, Feynman rules
  • Proca field; helicity states
  • Quantization of Abelian vector fields and quantum electrodynamics
  • Non-Abelian gauge theories: Yang-Mills fields
  • Faddeev-Popov ghosts
  • Slavnov-Taylor identities
  • Feynman rules for Yang-Mills fields
  • Perturbation theory

IV Renormalization of quantum field theories

  • Renormalizable and non-renormalizable field theories
  • Loop integrals and regularization in D dimensions
  • Renormalization in quantum electrodynamics
  • Dyson-Ward proof
  • Path integrals, Ward-Takahashi Identity
  • Becchi-Rouet-Stora transformation
  • Bogolyubov-Parasyuk-Hepp-Zimmermann renormalization proof of the quantum field theories
  • The renormalization group: Callan-Symanzik equations, running couplings and masses

Cross-language

201 045
Compulsory

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AncillaryCourses

Quantum Field Theory of Elementary Particles

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