I am a math student, studying P.D.E. of some EM theory.
I am new to field theory and I don't even know what a Lagrangian density, Hamiltonian density, or gauge field theory is.
Could you please introduce some books or notes to me?
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One of the standard textbooks to learn analytical mechanics and field theory from scratch is http://www.amazon.de/Classical-Mechanics-Herbert-Goldstein/dp/0321188977. Another book that I really liked is http://www.amazon.com/Lectures-Analytical-Mechanics-F-Gantmacher/dp/B000LZJN3E. These two introduce classical analytical mechanics, from which you can start to approach general field theories. – gented Sep 28 '15 at 13:43