Programme

Special Relativity and Electromagnetism.
Lorentz transformations, Minkowski plane, Poincarè and Lorentz groups. Covariant and
controvariant vectors, tensors, transformation law of the fields.
Relativistic Dynamics: four-velocity, four-momentum, Minkowski force.
Covariant formulation of Electromagnetism: transformation properties of the electric and magnetic fields,
electromagnetic field tensor, covariant formulation of the Maxwell equations, four-potential, gauge invariance.
Conservation laws: Maxwell stress tensor, energy-momentum tensor, conservation of energy,
momentum and angular momentum. Solution of the Maxwell equations for the four-potential in the vacuum in the Lorentz gauge.
Plane waves, radiation pressure. Lienard e Wiechert potentials. Radiated power. Thomson cross section. Compton effect.
Cerenkov effect.

Relativistic Quantum Mechanics
Klein-Gordon equation. Dirac equation, non-relativistic limit. Covariance of the Dirac equation.
Solutions of Dirac equation. Projectors for positive and negative energy solutions. Helicity. Chirality.

Quantum Field Theory
Quantization of the electromagnetic field in the radiation gauge. Creation and annihilation operators.
Heisenberg representation.
Lagrangian field theory, symmetry and conservation laws, Noether theorem. Field quantization. Lagrangian for a
real and complex scalar field, quantization. Lagrangian for a Dirac field, quantization.
Electromagnetic field, covariant quantization. Global and local invariance.
Interaction picture. S-matrix and its expansion. Wick theorem. Commutators and propagators for bosonic and fermionic fields.
Quantzation of the electromagnetic field.
Feynman diagrams and rules in QED.
Tree-level processes: e+e- - mu+ mu-, scattering by an external field.

Core Documentation

V. Barone: Relatività, Bollati Boringhieri.
F. Mandl, G. Shaw: Quantum Field Theory, John Wiley & Sons.

Type of delivery of the course

Lectures and recitations at the blackboard. Explanation of the theory presented via discussion of examples. In case of emergency due to COVID-19 pandemic the course will be given according to the University rules for the emergency.

Type of evaluation

The exam will consists of oral questions on both parts, Relativity and E.M. and Relativistic Q.M. and QFT. It is possible to waive the questions on Relativity and EM if the student pass the written test on this part that is going to be given at the end of the first part of the course. If the student does not pass the written test on Relativity and E.M. in the oral exam the student will be asked to solve a problem on Relativity o E.M. In case of emergency due to COVID-19 pandemic the exam will be given according to the University rules for the emergency.

Programme

Special Relativity and Electromagnetism.
Lorentz transformations, Minkowski plane, Poincarè and Lorentz groups. Covariant and
controvariant vectors, tensors, transformation law of the fields.
Relativistic Dynamics: four-velocity, four-momentum, Minkowski force.
Covariant formulation of Electromagnetism: transformation properties of the electric and magnetic fields,
electromagnetic field tensor, covariant formulation of the Maxwell equations, four-potential, gauge invariance.
Conservation laws: Maxwell stress tensor, energy-momentum tensor, conservation of energy,
momentum and angular momentum. Solution of the Maxwell equations for the four-potential in the vacuum in the Lorentz gauge.
Plane waves, radiation pressure. Lienard e Wiechert potentials. Radiated power. Thomson cross section. Compton effect.
Cerenkov effect.

Relativistic Quantum Mechanics
Klein-Gordon equation. Dirac equation, non-relativistic limit. Covariance of the Dirac equation.
Solutions of Dirac equation. Projectors for positive and negative energy solutions. Helicity. Chirality.

Quantum Field Theory
Quantization of the electromagnetic field in the radiation gauge. Creation and annihilation operators.
Heisenberg representation.
Lagrangian field theory, symmetry and conservation laws, Noether theorem. Field quantization. Lagrangian for a
real and complex scalar field, quantization. Lagrangian for a Dirac field, quantization.
Electromagnetic field, covariant quantization. Global and local invariance.
Interaction picture. S-matrix and its expansion. Wick theorem. Commutators and propagators for bosonic and fermionic fields.
Quantzation of the electromagnetic field.
Feynman diagrams and rules in QED.
Tree-level processes: e+e- - mu+ mu-, scattering by an external field.

Core Documentation

V. Barone: Relatività, Bollati Boringhieri.
F. Mandl, G. Shaw: Quantum Field Theory, John Wiley & Sons.

Type of delivery of the course

Lectures and recitations at the blackboard. Explanation of the theory presented via discussion of examples. In case of emergency due to COVID-19 pandemic the course will be given according to the University rules for the emergency.

Type of evaluation

The exam will consists of oral questions on both parts, Relativity and E.M. and Relativistic Q.M. and QFT. It is possible to waive the questions on Relativity and EM if the student pass the written test on this part that is going to be given at the end of the first part of the course. If the student does not pass the written test on Relativity and E.M. in the oral exam the student will be asked to solve a problem on Relativity o E.M. In case of emergency due to COVID-19 pandemic the exam will be given according to the University rules for the emergency.

Programme

Special Relativity and Electromagnetism.
Lorentz transformations, Minkowski plane, Poincarè and Lorentz groups. Covariant and
controvariant vectors, tensors, transformation law of the fields.
Relativistic Dynamics: four-velocity, four-momentum, Minkowski force.
Covariant formulation of Electromagnetism: transformation properties of the electric and magnetic fields,
electromagnetic field tensor, covariant formulation of the Maxwell equations, four-potential, gauge invariance.
Conservation laws: Maxwell stress tensor, energy-momentum tensor, conservation of energy,
momentum and angular momentum. Solution of the Maxwell equations for the four-potential in the vacuum in the Lorentz gauge.
Plane waves, radiation pressure. Lienard e Wiechert potentials. Radiated power. Thomson cross section. Compton effect.
Cerenkov effect.

Relativistic Quantum Mechanics
Klein-Gordon equation. Dirac equation, non-relativistic limit. Covariance of the Dirac equation.
Solutions of Dirac equation. Projectors for positive and negative energy solutions. Helicity. Chirality.

Quantum Field Theory
Quantization of the electromagnetic field in the radiation gauge. Creation and annihilation operators.
Heisenberg representation.
Lagrangian field theory, symmetry and conservation laws, Noether theorem. Field quantization. Lagrangian for a
real and complex scalar field, quantization. Lagrangian for a Dirac field, quantization.
Electromagnetic field, covariant quantization. Global and local invariance.
Interaction picture. S-matrix and its expansion. Wick theorem. Commutators and propagators for bosonic and fermionic fields.
Quantzation of the electromagnetic field.
Feynman diagrams and rules in QED.
Tree-level processes: e+e- - mu+ mu-, scattering by an external field.

Core Documentation

V. Barone: Relatività, Bollati Boringhieri.
F. Mandl, G. Shaw: Quantum Field Theory, John Wiley & Sons.

Type of delivery of the course

Lectures and recitations at the blackboard. Explanation of the theory presented via discussion of examples. In case of emergency due to COVID-19 pandemic the course will be given according to the University rules for the emergency.

Type of evaluation

The exam will consists of oral questions on both parts, Relativity and E.M. and Relativistic Q.M. and QFT. It is possible to waive the questions on Relativity and EM if the student pass the written test on this part that is going to be given at the end of the first part of the course. If the student does not pass the written test on Relativity and E.M. in the oral exam the student will be asked to solve a problem on Relativity o E.M. In case of emergency due to COVID-19 pandemic the exam will be given according to the University rules for the emergency.

Programme

Special Relativity and Electromagnetism.
Lorentz transformations, Minkowski plane, Poincarè and Lorentz groups. Covariant and
controvariant vectors, tensors, transformation law of the fields.
Relativistic Dynamics: four-velocity, four-momentum, Minkowski force.
Covariant formulation of Electromagnetism: transformation properties of the electric and magnetic fields,
electromagnetic field tensor, covariant formulation of the Maxwell equations, four-potential, gauge invariance.
Conservation laws: Maxwell stress tensor, energy-momentum tensor, conservation of energy,
momentum and angular momentum. Solution of the Maxwell equations for the four-potential in the vacuum in the Lorentz gauge.
Plane waves, radiation pressure. Lienard e Wiechert potentials. Radiated power. Thomson cross section. Compton effect.
Cerenkov effect.

Relativistic Quantum Mechanics
Klein-Gordon equation. Dirac equation, non-relativistic limit. Covariance of the Dirac equation.
Solutions of Dirac equation. Projectors for positive and negative energy solutions. Helicity. Chirality.

Quantum Field Theory
Quantization of the electromagnetic field in the radiation gauge. Creation and annihilation operators.
Heisenberg representation.
Lagrangian field theory, symmetry and conservation laws, Noether theorem. Field quantization. Lagrangian for a
real and complex scalar field, quantization. Lagrangian for a Dirac field, quantization.
Electromagnetic field, covariant quantization. Global and local invariance.
Interaction picture. S-matrix and its expansion. Wick theorem. Commutators and propagators for bosonic and fermionic fields.
Quantzation of the electromagnetic field.
Feynman diagrams and rules in QED.
Tree-level processes: e+e- - mu+ mu-, scattering by an external field.

Core Documentation

V. Barone: Relatività, Bollati Boringhieri.
F. Mandl, G. Shaw: Quantum Field Theory, John Wiley & Sons.

Type of delivery of the course

Lectures and recitations at the blackboard. Explanation of the theory presented via discussion of examples. In case of emergency due to COVID-19 pandemic the course will be given according to the University rules for the emergency.

Type of evaluation

The exam will consists of oral questions on both parts, Relativity and E.M. and Relativistic Q.M. and QFT. It is possible to waive the questions on Relativity and EM if the student pass the written test on this part that is going to be given at the end of the first part of the course. If the student does not pass the written test on Relativity and E.M. in the oral exam the student will be asked to solve a problem on Relativity o E.M. In case of emergency due to COVID-19 pandemic the exam will be given according to the University rules for the emergency.

Programme

Special Relativity and Electromagnetism.
Lorentz transformations, Minkowski plane, Poincarè and Lorentz groups. Covariant and
controvariant vectors, tensors, transformation law of the fields.
Relativistic Dynamics: four-velocity, four-momentum, Minkowski force.
Covariant formulation of Electromagnetism: transformation properties of the electric and magnetic fields,
electromagnetic field tensor, covariant formulation of the Maxwell equations, four-potential, gauge invariance.
Conservation laws: Maxwell stress tensor, energy-momentum tensor, conservation of energy,
momentum and angular momentum. Solution of the Maxwell equations for the four-potential in the vacuum in the Lorentz gauge.
Plane waves, radiation pressure. Lienard e Wiechert potentials. Radiated power. Thomson cross section. Compton effect.
Cerenkov effect.

Relativistic Quantum Mechanics
Klein-Gordon equation. Dirac equation, non-relativistic limit. Covariance of the Dirac equation.
Solutions of Dirac equation. Projectors for positive and negative energy solutions. Helicity. Chirality.

Quantum Field Theory
Quantization of the electromagnetic field in the radiation gauge. Creation and annihilation operators.
Heisenberg representation.
Lagrangian field theory, symmetry and conservation laws, Noether theorem. Field quantization. Lagrangian for a
real and complex scalar field, quantization. Lagrangian for a Dirac field, quantization.
Electromagnetic field, covariant quantization. Global and local invariance.
Interaction picture. S-matrix and its expansion. Wick theorem. Commutators and propagators for bosonic and fermionic fields.
Quantzation of the electromagnetic field.
Feynman diagrams and rules in QED.
Tree-level processes: e+e- - mu+ mu-, scattering by an external field.

Core Documentation

V. Barone: Relatività, Bollati Boringhieri.
F. Mandl, G. Shaw: Quantum Field Theory, John Wiley & Sons.

Type of delivery of the course

Lectures and recitations at the blackboard. Explanation of the theory presented via discussion of examples. In case of emergency due to COVID-19 pandemic the course will be given according to the University rules for the emergency.

Type of evaluation

The exam will consists of oral questions on both parts, Relativity and E.M. and Relativistic Q.M. and QFT. It is possible to waive the questions on Relativity and EM if the student pass the written test on this part that is going to be given at the end of the first part of the course. If the student does not pass the written test on Relativity and E.M. in the oral exam the student will be asked to solve a problem on Relativity o E.M. In case of emergency due to COVID-19 pandemic the exam will be given according to the University rules for the emergency.

Programme

Special Relativity and Electromagnetism.
Lorentz transformations, Minkowski plane, Poincarè and Lorentz groups. Covariant and
controvariant vectors, tensors, transformation law of the fields.
Relativistic Dynamics: four-velocity, four-momentum, Minkowski force.
Covariant formulation of Electromagnetism: transformation properties of the electric and magnetic fields,
electromagnetic field tensor, covariant formulation of the Maxwell equations, four-potential, gauge invariance.
Conservation laws: Maxwell stress tensor, energy-momentum tensor, conservation of energy,
momentum and angular momentum. Solution of the Maxwell equations for the four-potential in the vacuum in the Lorentz gauge.
Plane waves, radiation pressure. Lienard e Wiechert potentials. Radiated power. Thomson cross section. Compton effect.
Cerenkov effect.

Relativistic Quantum Mechanics
Klein-Gordon equation. Dirac equation, non-relativistic limit. Covariance of the Dirac equation.
Solutions of Dirac equation. Projectors for positive and negative energy solutions. Helicity. Chirality.

Quantum Field Theory
Quantization of the electromagnetic field in the radiation gauge. Creation and annihilation operators.
Heisenberg representation.
Lagrangian field theory, symmetry and conservation laws, Noether theorem. Field quantization. Lagrangian for a
real and complex scalar field, quantization. Lagrangian for a Dirac field, quantization.
Electromagnetic field, covariant quantization. Global and local invariance.
Interaction picture. S-matrix and its expansion. Wick theorem. Commutators and propagators for bosonic and fermionic fields.
Quantzation of the electromagnetic field.
Feynman diagrams and rules in QED.
Tree-level processes: e+e- - mu+ mu-, scattering by an external field.

Core Documentation

V. Barone: Relatività, Bollati Boringhieri.
F. Mandl, G. Shaw: Quantum Field Theory, John Wiley & Sons.

Type of delivery of the course

Lectures and recitations at the blackboard. Explanation of the theory presented via discussion of examples. In case of emergency due to COVID-19 pandemic the course will be given according to the University rules for the emergency.

Type of evaluation

The exam will consists of oral questions on both parts, Relativity and E.M. and Relativistic Q.M. and QFT. It is possible to waive the questions on Relativity and EM if the student pass the written test on this part that is going to be given at the end of the first part of the course. If the student does not pass the written test on Relativity and E.M. in the oral exam the student will be asked to solve a problem on Relativity o E.M. In case of emergency due to COVID-19 pandemic the exam will be given according to the University rules for the emergency.

Programme

Special Relativity and Electromagnetism.
Lorentz transformations, Minkowski plane, Poincarè and Lorentz groups. Covariant and
controvariant vectors, tensors, transformation law of the fields.
Relativistic Dynamics: four-velocity, four-momentum, Minkowski force.
Covariant formulation of Electromagnetism: transformation properties of the electric and magnetic fields,
electromagnetic field tensor, covariant formulation of the Maxwell equations, four-potential, gauge invariance.
Conservation laws: Maxwell stress tensor, energy-momentum tensor, conservation of energy,
momentum and angular momentum. Solution of the Maxwell equations for the four-potential in the vacuum in the Lorentz gauge.
Plane waves, radiation pressure. Lienard e Wiechert potentials. Radiated power. Thomson cross section. Compton effect.
Cerenkov effect.

Relativistic Quantum Mechanics
Klein-Gordon equation. Dirac equation, non-relativistic limit. Covariance of the Dirac equation.
Solutions of Dirac equation. Projectors for positive and negative energy solutions. Helicity. Chirality.

Quantum Field Theory
Quantization of the electromagnetic field in the radiation gauge. Creation and annihilation operators.
Heisenberg representation.
Lagrangian field theory, symmetry and conservation laws, Noether theorem. Field quantization. Lagrangian for a
real and complex scalar field, quantization. Lagrangian for a Dirac field, quantization.
Electromagnetic field, covariant quantization. Global and local invariance.
Interaction picture. S-matrix and its expansion. Wick theorem. Commutators and propagators for bosonic and fermionic fields.
Quantzation of the electromagnetic field.
Feynman diagrams and rules in QED.
Tree-level processes: e+e- - mu+ mu-, scattering by an external field.

Core Documentation

V. Barone: Relatività, Bollati Boringhieri.
F. Mandl, G. Shaw: Quantum Field Theory, John Wiley & Sons.

Type of delivery of the course

Lectures and recitations at the blackboard. Explanation of the theory presented via discussion of examples. In case of emergency due to COVID-19 pandemic the course will be given according to the University rules for the emergency.

Type of evaluation

The exam will consists of oral questions on both parts, Relativity and E.M. and Relativistic Q.M. and QFT. It is possible to waive the questions on Relativity and EM if the student pass the written test on this part that is going to be given at the end of the first part of the course. If the student does not pass the written test on Relativity and E.M. in the oral exam the student will be asked to solve a problem on Relativity o E.M. In case of emergency due to COVID-19 pandemic the exam will be given according to the University rules for the emergency.

Programme

Special Relativity and Electromagnetism.
Lorentz transformations, Minkowski plane, Poincarè and Lorentz groups. Covariant and
controvariant vectors, tensors, transformation law of the fields.
Relativistic Dynamics: four-velocity, four-momentum, Minkowski force.
Covariant formulation of Electromagnetism: transformation properties of the electric and magnetic fields,
electromagnetic field tensor, covariant formulation of the Maxwell equations, four-potential, gauge invariance.
Conservation laws: Maxwell stress tensor, energy-momentum tensor, conservation of energy,
momentum and angular momentum. Solution of the Maxwell equations for the four-potential in the vacuum in the Lorentz gauge.
Plane waves, radiation pressure. Lienard e Wiechert potentials. Radiated power. Thomson cross section. Compton effect.
Cerenkov effect.

Relativistic Quantum Mechanics
Klein-Gordon equation. Dirac equation, non-relativistic limit. Covariance of the Dirac equation.
Solutions of Dirac equation. Projectors for positive and negative energy solutions. Helicity. Chirality.

Quantum Field Theory
Quantization of the electromagnetic field in the radiation gauge. Creation and annihilation operators.
Heisenberg representation.
Lagrangian field theory, symmetry and conservation laws, Noether theorem. Field quantization. Lagrangian for a
real and complex scalar field, quantization. Lagrangian for a Dirac field, quantization.
Electromagnetic field, covariant quantization. Global and local invariance.
Interaction picture. S-matrix and its expansion. Wick theorem. Commutators and propagators for bosonic and fermionic fields.
Quantzation of the electromagnetic field.
Feynman diagrams and rules in QED.
Tree-level processes: e+e- - mu+ mu-, scattering by an external field.

Core Documentation

V. Barone: Relatività, Bollati Boringhieri.
F. Mandl, G. Shaw: Quantum Field Theory, John Wiley & Sons.

Type of delivery of the course

Lectures and recitations at the blackboard. Explanation of the theory presented via discussion of examples. In case of emergency due to COVID-19 pandemic the course will be given according to the University rules for the emergency.

Type of evaluation

The exam will consists of oral questions on both parts, Relativity and E.M. and Relativistic Q.M. and QFT. It is possible to waive the questions on Relativity and EM if the student pass the written test on this part that is going to be given at the end of the first part of the course. If the student does not pass the written test on Relativity and E.M. in the oral exam the student will be asked to solve a problem on Relativity o E.M. In case of emergency due to COVID-19 pandemic the exam will be given according to the University rules for the emergency.

Programme

Special Relativity and Electromagnetism.
Lorentz transformations, Minkowski plane, Poincarè and Lorentz groups. Covariant and
controvariant vectors, tensors, transformation law of the fields.
Relativistic Dynamics: four-velocity, four-momentum, Minkowski force.
Covariant formulation of Electromagnetism: transformation properties of the electric and magnetic fields,
electromagnetic field tensor, covariant formulation of the Maxwell equations, four-potential, gauge invariance.
Conservation laws: Maxwell stress tensor, energy-momentum tensor, conservation of energy,
momentum and angular momentum. Solution of the Maxwell equations for the four-potential in the vacuum in the Lorentz gauge.
Plane waves, radiation pressure. Lienard e Wiechert potentials. Radiated power. Thomson cross section. Compton effect.
Cerenkov effect.

Relativistic Quantum Mechanics
Klein-Gordon equation. Dirac equation, non-relativistic limit. Covariance of the Dirac equation.
Solutions of Dirac equation. Projectors for positive and negative energy solutions. Helicity. Chirality.

Quantum Field Theory
Quantization of the electromagnetic field in the radiation gauge. Creation and annihilation operators.
Heisenberg representation.
Lagrangian field theory, symmetry and conservation laws, Noether theorem. Field quantization. Lagrangian for a
real and complex scalar field, quantization. Lagrangian for a Dirac field, quantization.
Electromagnetic field, covariant quantization. Global and local invariance.
Interaction picture. S-matrix and its expansion. Wick theorem. Commutators and propagators for bosonic and fermionic fields.
Quantzation of the electromagnetic field.
Feynman diagrams and rules in QED.
Tree-level processes: e+e- - mu+ mu-, scattering by an external field.

Core Documentation

V. Barone: Relatività, Bollati Boringhieri.
F. Mandl, G. Shaw: Quantum Field Theory, John Wiley & Sons.

Type of delivery of the course

Lectures and recitations at the blackboard. Explanation of the theory presented via discussion of examples. In case of emergency due to COVID-19 pandemic the course will be given according to the University rules for the emergency.

Type of evaluation

The exam will consists of oral questions on both parts, Relativity and E.M. and Relativistic Q.M. and QFT. It is possible to waive the questions on Relativity and EM if the student pass the written test on this part that is going to be given at the end of the first part of the course. If the student does not pass the written test on Relativity and E.M. in the oral exam the student will be asked to solve a problem on Relativity o E.M. In case of emergency due to COVID-19 pandemic the exam will be given according to the University rules for the emergency.

Programme

Special Relativity and Electromagnetism.
Lorentz transformations, Minkowski plane, Poincarè and Lorentz groups. Covariant and
controvariant vectors, tensors, transformation law of the fields.
Relativistic Dynamics: four-velocity, four-momentum, Minkowski force.
Covariant formulation of Electromagnetism: transformation properties of the electric and magnetic fields,
electromagnetic field tensor, covariant formulation of the Maxwell equations, four-potential, gauge invariance.
Conservation laws: Maxwell stress tensor, energy-momentum tensor, conservation of energy,
momentum and angular momentum. Solution of the Maxwell equations for the four-potential in the vacuum in the Lorentz gauge.
Plane waves, radiation pressure. Lienard e Wiechert potentials. Radiated power. Thomson cross section. Compton effect.
Cerenkov effect.

Relativistic Quantum Mechanics
Klein-Gordon equation. Dirac equation, non-relativistic limit. Covariance of the Dirac equation.
Solutions of Dirac equation. Projectors for positive and negative energy solutions. Helicity. Chirality.

Quantum Field Theory
Quantization of the electromagnetic field in the radiation gauge. Creation and annihilation operators.
Heisenberg representation.
Lagrangian field theory, symmetry and conservation laws, Noether theorem. Field quantization. Lagrangian for a
real and complex scalar field, quantization. Lagrangian for a Dirac field, quantization.
Electromagnetic field, covariant quantization. Global and local invariance.
Interaction picture. S-matrix and its expansion. Wick theorem. Commutators and propagators for bosonic and fermionic fields.
Quantzation of the electromagnetic field.
Feynman diagrams and rules in QED.
Tree-level processes: e+e- - mu+ mu-, scattering by an external field.

Core Documentation

V. Barone: Relatività, Bollati Boringhieri.
F. Mandl, G. Shaw: Quantum Field Theory, John Wiley & Sons.

Type of delivery of the course

Lectures and recitations at the blackboard. Explanation of the theory presented via discussion of examples. In case of emergency due to COVID-19 pandemic the course will be given according to the University rules for the emergency.

Type of evaluation

The exam will consists of oral questions on both parts, Relativity and E.M. and Relativistic Q.M. and QFT. It is possible to waive the questions on Relativity and EM if the student pass the written test on this part that is going to be given at the end of the first part of the course. If the student does not pass the written test on Relativity and E.M. in the oral exam the student will be asked to solve a problem on Relativity o E.M. In case of emergency due to COVID-19 pandemic the exam will be given according to the University rules for the emergency.

Programme

Special Relativity and Electromagnetism.
Lorentz transformations, Minkowski plane, Poincarè and Lorentz groups. Covariant and
controvariant vectors, tensors, transformation law of the fields.
Relativistic Dynamics: four-velocity, four-momentum, Minkowski force.
Covariant formulation of Electromagnetism: transformation properties of the electric and magnetic fields,
electromagnetic field tensor, covariant formulation of the Maxwell equations, four-potential, gauge invariance.
Conservation laws: Maxwell stress tensor, energy-momentum tensor, conservation of energy,
momentum and angular momentum. Solution of the Maxwell equations for the four-potential in the vacuum in the Lorentz gauge.
Plane waves, radiation pressure. Lienard e Wiechert potentials. Radiated power. Thomson cross section. Compton effect.
Cerenkov effect.

Relativistic Quantum Mechanics
Klein-Gordon equation. Dirac equation, non-relativistic limit. Covariance of the Dirac equation.
Solutions of Dirac equation. Projectors for positive and negative energy solutions. Helicity. Chirality.

Quantum Field Theory
Quantization of the electromagnetic field in the radiation gauge. Creation and annihilation operators.
Heisenberg representation.
Lagrangian field theory, symmetry and conservation laws, Noether theorem. Field quantization. Lagrangian for a
real and complex scalar field, quantization. Lagrangian for a Dirac field, quantization.
Electromagnetic field, covariant quantization. Global and local invariance.
Interaction picture. S-matrix and its expansion. Wick theorem. Commutators and propagators for bosonic and fermionic fields.
Quantzation of the electromagnetic field.
Feynman diagrams and rules in QED.
Tree-level processes: e+e- - mu+ mu-, scattering by an external field.

Core Documentation

V. Barone: Relatività, Bollati Boringhieri.
F. Mandl, G. Shaw: Quantum Field Theory, John Wiley & Sons.

Type of delivery of the course

Lectures and recitations at the blackboard. Explanation of the theory presented via discussion of examples. In case of emergency due to COVID-19 pandemic the course will be given according to the University rules for the emergency.

Type of evaluation

The exam will consists of oral questions on both parts, Relativity and E.M. and Relativistic Q.M. and QFT. It is possible to waive the questions on Relativity and EM if the student pass the written test on this part that is going to be given at the end of the first part of the course. If the student does not pass the written test on Relativity and E.M. in the oral exam the student will be asked to solve a problem on Relativity o E.M. In case of emergency due to COVID-19 pandemic the exam will be given according to the University rules for the emergency.

Programme

Special Relativity and Electromagnetism.
Lorentz transformations, Minkowski plane, Poincarè and Lorentz groups. Covariant and
controvariant vectors, tensors, transformation law of the fields.
Relativistic Dynamics: four-velocity, four-momentum, Minkowski force.
Covariant formulation of Electromagnetism: transformation properties of the electric and magnetic fields,
electromagnetic field tensor, covariant formulation of the Maxwell equations, four-potential, gauge invariance.
Conservation laws: Maxwell stress tensor, energy-momentum tensor, conservation of energy,
momentum and angular momentum. Solution of the Maxwell equations for the four-potential in the vacuum in the Lorentz gauge.
Plane waves, radiation pressure. Lienard e Wiechert potentials. Radiated power. Thomson cross section. Compton effect.
Cerenkov effect.

Relativistic Quantum Mechanics
Klein-Gordon equation. Dirac equation, non-relativistic limit. Covariance of the Dirac equation.
Solutions of Dirac equation. Projectors for positive and negative energy solutions. Helicity. Chirality.

Quantum Field Theory
Quantization of the electromagnetic field in the radiation gauge. Creation and annihilation operators.
Heisenberg representation.
Lagrangian field theory, symmetry and conservation laws, Noether theorem. Field quantization. Lagrangian for a
real and complex scalar field, quantization. Lagrangian for a Dirac field, quantization.
Electromagnetic field, covariant quantization. Global and local invariance.
Interaction picture. S-matrix and its expansion. Wick theorem. Commutators and propagators for bosonic and fermionic fields.
Quantzation of the electromagnetic field.
Feynman diagrams and rules in QED.
Tree-level processes: e+e- - mu+ mu-, scattering by an external field.

Core Documentation

V. Barone: Relatività, Bollati Boringhieri.
F. Mandl, G. Shaw: Quantum Field Theory, John Wiley & Sons.

Type of delivery of the course

Lectures and recitations at the blackboard. Explanation of the theory presented via discussion of examples. In case of emergency due to COVID-19 pandemic the course will be given according to the University rules for the emergency.

Type of evaluation

The exam will consists of oral questions on both parts, Relativity and E.M. and Relativistic Q.M. and QFT. It is possible to waive the questions on Relativity and EM if the student pass the written test on this part that is going to be given at the end of the first part of the course. If the student does not pass the written test on Relativity and E.M. in the oral exam the student will be asked to solve a problem on Relativity o E.M. In case of emergency due to COVID-19 pandemic the exam will be given according to the University rules for the emergency.