Dirac Slash
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Dirac Slash

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),

using the Einstein summation notation where γ are the gamma matrices.

Identities

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,

where

is the Levi-Civita symbol.

With four-momentum

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.

See also

References

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

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