Special Relativity

• Κύριος συγγραφέας: Faraoni, Valerio (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2013.
• Σειρά: Undergraduate Lecture Notes in Physics,
• Θέματα: Physics.; Mathematical physics.; Gravitation.; Classical and Quantum Gravitation, Relativity Theory.; Mathematical Applications in the Physical Sciences.

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...

Πίνακας περιεχομένων:

• 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.