>>14213639Landau+Lifshitz. They have separate books on both field theories. Their books are on archive
https://archive.org/details/landau-and-lifshitz-physics-textbooks-seriesYou might be able to find some other classic books on this.
>All the four-tensor stuff has me stumped.This is just a matter of convention and algebra. Though a lot of physicists don't really have very good books on Tensors and the "transform like a tensor" thing they like to say really doesn't help. At the same time math books on it seem to be overboard in their technicality for a beginners and really don't have as many examples as they should. You'll see what I mean. Some samples:
https://web.math.princeton.edu/~nelson/books/ta.pdfhttp://www.ipgp.fr/~tarantola/Files/Professional/Teaching/Diverse/TensorsForBeginners/Text/Tensors.pdfhttps://web.iitd.ac.in/~pmvs/courses/mcl702/tensors.pdfhttps://oaktrust.library.tamu.edu/bitstream/handle/1969.1/2502/IntroductionToVectorsAndTensorsVol1.pdfAnd then there's always reference to indexes, summation conventions, and classifying tensors immediately when that should come later.
So give you something to think about in . Typically a vector can be represented by a column vector . We can take a row vector and define a linear transformation
.
You might recognize this as the dot product. But here we fixed the row vector and we can take any column vector. The transformation just multiplies the fixed row vector with any column vector you want and you get a real number. This is the most basic form of a tensor. It takes a vector in and calculates a scalar value.