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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| Hlavní autor: | |
|---|---|
| Médium: | Livre numérique |
| Jazyk: | Anglais |
| Vydáno: |
Cham :
Springer International Publishing : Imprint: Springer
[20..].
Cham : Springer Nature |
| Edice: | Undergraduate Lecture Notes in Physics
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| On-line přístup: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
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Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Special Relativity, Valerio Faraoni, Cham, Springer International Publishing, Springer, 2013, 1 vol. (XVIII-304 p.), Undergraduate Lecture Notes in Physics, 978-3-319-01106-6 |
Obsah:
- 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