A Primer in Tensor Analysis and Relativity

This undergraduate textbook provides a simple, concise introduction to tensor algebra and analysis, as well as special and general relativity. With a plethora of examples, explanations, and exercises, it forms a well-rounded didactic text that will be useful for any related course.

The book is divided into three main parts, all based on lecture notes that have been refined for classroom teaching over the past two decades. Part I provides students with a comprehensive overview of tensors. Part II links the very introductory first part and the relatively advanced third part, demonstrating the important intermediate-level applications of tensor analysis. Part III contains an extended discussion of general relativity, and includes material useful for students interested primarily in quantum field theory and quantum gravity.

Tailored to the undergraduate, this textbook offers explanations of technical material not easily found or detailed elsewhere, includingan understandable description of Riemann normal coordinates and conformal transformations. Future theoretical and experimental physicists, as well as mathematicians, will thus find it a wonderful first read on the subject.

Designed for undergraduate students looking to enter the field of quantum gravity and particle physics Fills a gap in the often outdated and overly complicated existing literature Includes a plethora of examples and exercises

Autorentext
Ilya L. Shapiro is a professor (professor Titular) at the Departamento de Fisica at Universidade Federal de Juiz de Fora, in Minas Gerais, Brazil. His teaching background ranges from the graduate and postgraduate level down to undergraduate and high school courses, giving him a broad perspective and authoritative voice on the subject of teaching physics. Shapiro was a member of the Russian Gravitational Association from 1988 to 1998. He is currently part of the American Mathematical Society, the Brazilian Physical Society, and as of 2015, the Accessory Committee of Physics and Astronomy in CNPq (Funding Agency of Brazilian Ministry of Science and Technology) since 2015. He is the author of more than 140 papers as well as a coauthor on the well-known 1992 book on quantum field theory and quantum gravity, Effective Action in Quantum Gravity.

Inhalt
Acknowledgements.- Preface.- Part I: Tensor Algebra and Analysis.- 1: Linear spaces, vectors and tensors.- 2: Operations over tensors, metric tensor.- 3: Symmetric, skew(anti) symmetric tensors and determinants.- 4: Curvilinear coordinates, local coordinate transformations.- 5: Derivatives of tensors, covariant derivates.- 6: Grad, div, rot and relations between them.- 7: Grad, div, rot and in cylindric and spherical coordinates.- 8: Curvilinear, surface and D-dimensional integrals.- 9: Theorems of Green, Stokes and Gauss.- 10: Solutions to the exercises from Part 1.- Part II: Elements of Electrodynamics and Special Relativity.- 11 Maxwell equations and Lorentz transformations.- 12 Laws of relativistic mechanics.- 13 Maxwell equations in relativistic form.- Part III Applications to General Relativity.- 14 Equivalence principle, covariance and curvature tensor.- 15 Einstein equations, Schwarzschild solution and gravitational waves.- 16 Basic elements of cosmology.- 17 Special sections.- Index.