Feynman slash notation


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[1]). If A is a covariant vector (i.e., a 1-form),

where γ are the gamma matrices. Using the Einstein summation notation, the expression is simply


Identities edit

Using the anticommutators of the gamma matrices, one can show that for any   and  ,


where   is the identity matrix in four dimensions.

In particular,


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
  •   is the Minkowski metric
  •   is a scalar.

With four-momentum edit

This section uses the (+ − − −) metric signature. 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 contravariant four-momentum in natural units,


we see explicitly that


Similar results hold in other bases, such as the Weyl basis.

See also edit

References edit

  1. ^ Weinberg, Steven (1995), The Quantum Theory of Fields, vol. 1, Cambridge University Press, p. 358 (380 in polish edition), ISBN 0-521-55001-7