Abstract index notation
From Wikipedia
Abstract index notation is a mathematical notation for tensors, and more generally spinors, which uses indices to indicate their type. This is the current mathematics collaboration of the week! Please help improve it to featured article standard. ... In mathematics and physics, in particular in the theory of the orthogonal groups, spinors are certain kinds of mathematical objects (group representations of Spin(N), roughly speaking) similar to vectors, but which change sign under a rotation of radians. ...
Thus the index isn't related to any coordinate system and doesn't take numerical values. It was designed by Roger Penrose to compensate for the difficulty to describe contractions in modern abstract tensor notation, without losing the intrinsically geometric viewpoint. The notation has been extended by Predrag Cvitanović. Sir Roger Penrose OM (born August 8, 1931) is an English mathematical physicist. ...
The word contraction when used alone, has several possible meanings in the English language. ...
References
- Roger Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe, 2004, has a chapter explaining it.
- Roger Penrose and Wolfgang Rindler, Spinors and space-time, volume I, two-spinor calculus and relativistic fields.
External links
A group theory book (http://www.nbi.dk/GroupTheory/). Explains the notation.
