in Condensed Matter, Electromagnetism, and Gravitation
- Basics
- Galilean Invariance of Newtonian Mechanics
- Translations
- Rotations
- Galilei Boosts
- Galilei Group
- Lorentz Invariance of Maxwell Equations
- Lorentz Boosts**
- Lorentz Group
- Infinitesimal Lorentz Transformations
- Generators of Group Transformations
- Group Multiplication and Lie Algebra
- Vector-, Tensor-, and Scalar Fields
- Discrete Lorentz Transformations
- Poincare group
- Differential Operators for Lorentz Transformations
- Vector and Tensor Operators
- Behavior of Vectors and Tensors under Finite Lorentz Transformations
- Rotations*
- Lorentz Boosts
- Lorentz Group
- Relativistic Point Mechanics
- Quantum Mechanics
- Relativistic Particles in Electromagnetic Field
- Dirac Particles and Fields
- Energy-Momentum Tensor
- Point Particles
- Perfect Fluid
- Electromagnetic Field
- Angular Momentum and Spin
- Spacetime-Dependent Lorentz Transformations
- Angular Velocities
- Angular Gradients
- Appendix 1A Tensor Identities
- Product Formulas
- Determinants
- Galilean Invariance of Newtonian Mechanics
- Action Approach
- Continuous Symmetries and Conservation Laws. Noether’s Theorem
- Multivalued Gauge Transformations in Magnetostatics
- Multivalued Fields in Superfluids and Superconductors
- Dynamics of Superfluids
- Dynamics of Charged Superfluid and Superconductor
- Relativistic Magnetic Monopoles and Electric Charge Confinement
- Multivalued Mapping from Ideal Crystals to Crystals with Defects
- Defect Melting
- Relativistic Mechanics in Curvilinear Coordinates
- Torsion and Curvature from Defects
- Curvature and Torsion from Embedding
- Multivalued Mapping Principle
- Field Equations of Gravitation
- Minimally Coupled Fields of Integer Spin
- Particles with Half-Integer Spin
- Covariant Conservation Law
- Gravitation of Spinning Matter as a Gauge Theory
- Evanescent Properties of Torsion in Gravity
- Teleparallel Theory of Gravitation
- Emerging Gravity