MULTIVALUED FIELDS**

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
• 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