Abstract index notation is a mathematical notation for tensors, and more generally spinors, which uses indices to indicate their type.
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 .
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 . Explains the notation.