Feynman slash notation
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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. 1-form,
using the Einstein summation notation where γ are the gamma matrices.
[edit] Identities
Using the anticommutators of the gamma matrices, one can show that for any aμ,
In particular,
Further identities can be read off directly from the gamma matrix identities by replacing the metric tensor with inner products. For example,
-
![\operatorname{tr}(a\!\!\!/b\!\!\!/c\!\!\!/d\!\!\!/) = 4 \left[(a\cdot b)(c \cdot d) - (a \cdot c)(b \cdot d) + (a \cdot d)(b \cdot c) \right]](../../../math/c/e/3/ce302316cea8669f4de057e0aaed113f.png)
.
- where
is the Levi-Civita symbol.
[edit] See also
[edit] References
- Halzen, Francis; Martin, Alan (1984). Quarks & Leptons: An Introductory Course in Modern Particle Physics. John Wiley & Sons. ISBN 0471887412.
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