In the study of Dirac fields in quantum field theory, Richard Feynman invented the convenient Feynman slash notation (less commonly known as the Dirac slash notation). If A is a covariant vector (i.e., a 1-form),
using the Einstein summation notation where γ are the gamma matrices.
Using the anticommutators of the gamma matrices, one can show that for any and ,
where is the identity matrix in four dimensions.
Further identities can be read off directly from the gamma matrix identities by replacing the metric tensor with inner products. For example,
- is the Levi-Civita symbol.
Often, when using the Dirac equation and solving for cross sections, one finds the slash notation used on four-momentum: using the Dirac basis for the gamma matrices,
as well as the definition of four-momentum,
we see explicitly that
Similar results hold in other bases, such as the Weyl basis.
- Halzen, Francis; Martin, Alan (1984). Quarks & Leptons: An Introductory Course in Modern Particle Physics. John Wiley & Sons. ISBN 0-471-88741-2.