Special Relativity

This book offers an essential bridge between college-level introductions and advanced graduate-level books on special relativity. It begins at an elementary level, presenting and discussing the basic concepts normally covered in college-level works, including the Lorentz transformation. Subsequent c...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Faraoni, Valerio (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Springer, 2013.
Edición:1st ed. 2013.
Colección:Undergraduate Lecture Notes in Physics,
Temas:
Gravitation.
Mathematical physics.
Classical and Quantum Gravity.
Mathematical Physics.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • Fundamentals of Special Relativity
  • Introduction
  • The Principle of Relativity
  • Groups-the Galilei group
  • Galileian law of addition of velocities
  • The lesson from electromagnetism
  • The postulates of Special Relativity
  • Consequences of the postulates
  • Conclusion
  • Problems
  • The Lorentz transformation
  • Introduction
  • The Lorentz transformation
  • Derivation of the Lorentz transformation
  • Mathematical properties of the Lorentz transformation
  • Absolute speed limit and causality
  • Length contraction from the Lorentz transformation
  • Time dilation from the Lorentz transformation
  • Transformation of velocities and accelerations in Special Relativity
  • Matrix representation of the Lorentz transformation
  • The Lorentz group
  • The Lorentz transformation as a rotation by an imaginary angle with imaginary time
  • The GPS system
  • Conclusion
  • Problems
  • The 4-dimensional world view
  • Introduction
  • The 4-dimensional world
  • Spacetime diagrams
  • Conclusion
  • Problems
  • The formalism of tensors
  • Introduction
  • Vectors and tensors
  • Contravariant and covariant vectors
  • Contravariant and covariant tensors
  • Tensor algebra
  • Tensor fields
  • Index-free description of tensors
  • The metric tensor
  • The Levi-Civita symbol and tensor densities
  • Conclusion
  • Problems
  • Tensors in Minkowski spacetime
  • Introduction
  • Vectors and tensors in Minkowski spacetime
  • The Minkowski metric
  • Scalar product and length of a vector in Minkowski spacetime
  • Raising and lowering tensor indices
  • Causal nature of 4-vectors
  • Hypersurfaces
  • Gauss' theorem
  • Conclusion
  • Problems
  • Relativistic mechanics
  • Introduction
  • Relativistic dynamics of massive particles
  • The relativistic force
  • Angular momentum of a particle
  • Particle systems
  • Conservation of mass-energy
  • Conclusion
  • Problems
  • Relativistic optics
  • Introduction
  • Relativistic optics: null rays
  • The drag effect
  • The Doppler effect
  • Aberration
  • Relativistic beaming
  • Visual appearance of extended objects
  • Conclusion
  • Problems
  • Measurements in Minkowski spacetime
  • Introduction
  • Energy of a particle measured by an observer
  • Frequency measured by an observer
  • A more systematic treatment of measurement
  • The 3+1 splitting
  • Conclusion
  • Problems
  • Matter in Minkowski spacetime
  • Introduction
  • The energy-momentum tensor
  • Covariant conservation
  • Energy conditions
  • Angular momentum
  • Perfect fluids
  • The scalar field
  • The electromagnetic field
  • Conclusion
  • Problems
  • Special Relativity in arbitrary coordinates
  • Introduction
  • The covariant derivative
  • Spacetime curves and covariant derivative
  • Physics in Minkowski spacetime revisited
  • Conclusions
  • Problems
  • Solutions to selected problems
  • References
  • Index.

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