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Special Relativity

Author(s):
Publisher:

Springer

Pages: 304
Further Actions:

Recommend to library

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Paperback - 9783319011066

23 August 2013

$49.00

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Ebook - 9783319011073

15 August 2013

$34.99

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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...

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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 chapters introduce the four-dimensional worldview implied by the Lorentz transformations, mixing time and space coordinates, before continuing on to the formalism of tensors, a topic usually avoided in lower-level courses. The book’s second half addresses a number of essential points, including the concept of causality; the equivalence between mass and energy, including applications; relativistic optics; and measurements and matter in Minkowski space-time. The closing chapters focus on the energy-momentum tensor of a continuous distribution of mass-energy and its co-variant conservation; angular momentum; a discussion of the scalar field of perfect fluids and the Maxwell field; and general coordinates.

Every chapter is supplemented by a section with numerous exercises, allowing readers to practice the theory. These exercises constitute an essential part of the textbook, and the solutions to approximately half of them are provided in the appendix.

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Serves as a textbook at intermediate level between college-level introductions and more advanced textbooks requiring many prerequisites

Includes topics that are not usually included in standard textbooks on special relativity such as, for example, the theory of measurement in Minkowski spacetime

Has a chapter devoted to modern applications of Special Relativity, such as GPS, PET scanners, and other medical instruments

Contains a section with numerous exercises to practice the theory in each chapter

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.

From the reviews:“The book is one of the best texts in special relativity designed for readers between the college-level and advanced level. … A number of useful and new examples is added at the end of every chapter of the book. … A very useful table of constants is added at the end of the book. … The book represents one of the best conspects in special relativity and is useful for professors of special relativity. It is good for students and every other reader.” (Alex Gaina, zbMATH, Vol. 1277, 2014)
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Valerio Faraoni earned a BSc in Physics (Laurea in Fisica) at the University of Pavia, Italy, and an MSc and PhD (1991) in Astrophysics under the supervision of Prof. George F.R. Ellis at the International School for Advanced Studies in Trieste, Italy (www.sissa.it). He has held various research and teaching appointments at the University of Victoria, B.C., the Inter-University Centre for Astronomy and Astrophysics in Pune, India, the Free University of Brussels, Belgium, and the University of Northern British Columbia. He came to Bishop's University in 2005, where he is currently an Associate Professor in the physics department.

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Valerio Faraoni earned a BSc in Physics (Laurea in Fisica) at the University of Pavia, Italy, and an MSc and PhD (1991) in Astrophysics under the supervision of Prof. George F.R. Ellis at the International School for Advanced Studies in Trieste, Italy (www.sissa.it). He has held various research and teaching appointments at the University of Victoria, B.C., the Inter-University Centre for Astronomy and Astrophysics in Pune, India, the Free University of Brussels, Belgium, and the University of Northern British Columbia. He came to Bishop's University in 2005, where he is currently an Associate Professor in the physics department.

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