Special Relativity

Topics: Historical development and the origins of SR, Lorentz Transformations, relativistic kinematics (length contraction, time dilations, etc.), relativistic optics, Minkowski spacetime, relativistic particle mechanics (and four-vector technology), tensors, electromagnetism in covariant form, introduction to classical field theory, introduction to General Relativity.

Grading: 30% Midterm I, 30% Midterm II, 40% Final Exam.

Textbooks:

--  Wolfgang Rindler, Relativity: Special, General, and Cosmological, Oxford University Press, 2006. The first seven chapters.

-- John David Jackson, Classical Electrodynamics, Wiley, 1999. Chapters 11 and 12.

--  Robert Resnick, Introduction to Special Relativity, Wiley, 1968.

Additional sources:  

--  Bernard Schutz, A First Course in General Relativity, Cambridge University Press, 2009.

--  James Hartle, An Introduction to Einstein's General Relativity, Pearson Education Limited, 2014.

--  Hans Stephani, An Introduction to Special and General Relativity, Cambridge University Press, 2004. 

--  Leonard Susskind (and Art Friedman), Special Relativity and Classical Field Theory: The Theoretical Minimum, Allen Lane, 2017.

--  John Archibald Wheeler (with Edwin F. Taylor), Spacetime Physics: Introduction to Special Relativity, W. H. Freeman and Company, 1992.

--  L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields. Butterworth-Heinemann, 1994.

Lecture notes: 

Lecture 1:    Introduction, history, motivation.

Lecture 2:    Simultaneity, Lorentz transformations, Minkowski diagrams

Lecture 3:    Relativistic kinematics: Length contraction, time dilation, twin paradox

Lecture 3 (extra): The twin "paradox".

Lecture 4:    Acceleration, relativistic optics.

Lecture 5:    Four-vectors, tensors.

Lecture 6:    Four velocity, energy-momentum, relativistic mechanics, E=mc2.

Lecture 7:    Relativistic mechanics cont.

Lecture 8:    Covariant EMT, gauge transformations.

Lecture 9:    Lagrangian formalism of EMT, classical field theory.

Lecture 10:  Lagrangian formalism cont., Lorentz group.

Lecture 11:  Lorentz group cont., Thomas precession.

Lecture 12:  Introduction to General Relativity.

Sample problem sets:

Set 1.     Set 6.

Set 2. Set 7.

Set 3. Set 8.

Set 4. Set 9.

Set 5. Set 10.

Sample exams: 

Midterm-1

Midterm-2

Final