5
$\begingroup$

I am in a General Relativity class, and I am finding the usual tensor notation very difficult to think about -- it seems like there are too many names to express something simple. E.g., I think of the equation X^\mu_\nu = \eta_{\nu\nu'}X^{\mu\nu'} something like this:

 +---+       +---+ -| X |-   =  | X |-  +---+       |   |----+-----+              +---+    | eta |                    ---+-----+ 

I don't know, it's just a sketch (and doesn't handle the punning of using indices to represent different bases, for example). But I'm interested in all alternatives; what notations are available to make tensors easier to think about?

  • 0
    If you know about category theory then you'll be interested to know that diagrams like this can be used not just for linear maps but for morphisms in any "monoidal category". A good place to start might be [here](http://www.mscs.dal.ca/~selinger/papers/graphical.pdf).2014-12-15

1 Answers 1

1

As Rahul mentioned in a comment, what you are after seems to be essentially Penrose's diagrammatic tensor notation. Unfortunately it is a bit hard to find "live" use of the notation: graphical notations are really hard to typeset and so for ease of publication most articles in the literature are written using index notation instead. Besides Penrose's books and articles, the only publication I know that uses (some variant of) this notation is Predrag Cvitanović's group theory book which calls it "birdtrack" notation.