1 Special Relativity: A Recall
– 1.1 Introduction
– 1.2 Classical Mechanics
– 1.3 Hints Toward Relativity
– 1.4 Relativistic Spacetime
– 1.5 Lorentz Vectors and Tensors
– 1.6 Particle Dynamics
2 Group Transformations
– 2.1 Transformation Groups
– 2.2 Orthogonal Transformations
– 2.3 The Group of Rotations
– 2.4 The Poincaré Group
– 2.5 The Lorentz Group
3 Introducing Fields
– 3.1 The Standard Prototype
– 3.2 Non-Material Fields
– 3.3 Wavefields
– 3.4 Internal Transformations
4 General Formalism
– 4.1 Lagrangian Approach
– 4.2 The First Noether Theorem
– 4.3 The Second Noether Theorem
– 4.4 Topological Conservation Laws
5 Vector Fields
– 5.1 Real Vector Fields
– 5.2 Complex Vector Fields
6 Electromagnetic Field
– 6.1 Maxwell’s Equations
– 6.2 Transformations of E and H
– 6.3 Covariant Form of Maxwell’s Equations
– 6.4 Lagrangian,Spin, Energy
– 6.5 Motion of a Charged Particle
– 6.6 Electrostatics and Magnetostatics
– 6.7 Electromagnetic Waves
7 Scalar Fields
– 7.1 Real Scalar Fields
– 7.2 Complex Scalar Fields
8 Dirac Fields
– 8.1 Dirac Equation
– 8.2 Non-Relativistic Limit: Pauli Equation
– 8.3 Covariance
– 8.4 Lagrangian Formalism
– 8.5 Parity
– 8.6 Charge Conjugation
– 8.7 Time Reversal and CPT
9 Gauge Fields
– 9.1 Introduction
– 9.2 The Notion of Gauge Symmetry
– 9.3 Global Transformations
– 9.4 Local Transformations
– 9.5 Local Noether Theorem
– 9.6 Field Strength and Bianchi Identity
– 9.7 Gauge Lagrangian and Field Equation
– 9.8 Final Remarks
10 Gravitational Field
– 10.1 General Concepts
– 10.2 The Equivalence Principle
– 10.3 Pseudo-Riemannian Metric
– 10.4 The Notion of Connection
– 10.5 Curvature and Torsion
– 10.6 The Levi-Civita Connection
– 10.7 Geodesics
– 10.8 Bianchi Identities
– 10.9 Einstein’s Field Equations
– 10.10 The Schwarzschild Solution
- Professor: Sérgio Novaes