tensor(s) to be differentiated and a line joined from the circle pointing downwards to represent the lower index of the derivative. Tensor manipulation The diagrammatic notation is useful in manipulating tensor algebra. It usually involves a few simple "identities" of tensor manipulations. For example, , where n is the number of dimensions, is a common "identity". Riemann curvature tensor The Ricci and Bianchi identities given in terms of the Riemann curvature tensor illustrate the power of the notation Extensions The notation has been extended with support for spinors and twistors. See also Abstract index notation Angular momentum diagrams (quantum mechanics) Braided monoidal category Categorical quantum mechanics uses tensor diagram notation Matrix product state uses Penrose graphical notation Ricci calculus Spin networks Trace diagram Notes Tensors Theoretical physics Mathematical notation Diagram algebras