This should not be confused with a typographically similar convention used to distinguish between tensor index notation and the closely related but distinct basis-independent abstract index notation.
32.
The following is only an introduction to the concept : index notation is used in more detail in mathematics ( particularly in the representation and manipulation of tensor operations ).
33.
Cartesian tensors use tensor index notation, in which the variance may be glossed over and is often ignored, since the components remain unchanged by raising and lowering indices.
34.
In particular, in abstract index notation, the set of Maxwell's equations ( in the Lorenz gauge ) may be written ( in Gaussian units ) as follows:
35.
See also Ricci calculus for a summary of tensor index notations, and raising and lowering indices for definition of superscript and subscript indices, and how to switch between them.
36.
Note that physicists often refer to this matrix or the coordinates g _ { \ mu \ nu } themselves as the metric ( see, however, abstract index notation ).
37.
The Levi-Civita symbol allows the determinant of a square matrix, and the cross product of two vectors in three-dimensional Euclidean space, to be expressed in index notation.
38.
"' Abstract index notation "'is a mathematical notation for tensors and spinors that uses indices to indicate their types, rather than their components in a particular basis.
39.
If abstract index notation is used also for spinors then these will carry a spinorial index and the column matrices and the Dirac gamma as a matrix which additionally carries a Lorentzian index.
40.
This can be useful when manipulating indices, such as using index notation to verify vector calculus identities or identities of the Kronecker delta and Levi-Civita symbol ( see also below ).
