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),

${\displaystyle {A\!\!\!/}\ {\stackrel {\mathrm {def} }{=}}\ \gamma ^{0}A_{0}+\gamma ^{1}A_{1}+\gamma ^{2}A_{2}+\gamma ^{3}A_{3}}$

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

${\displaystyle {A\!\!\!/}\ {\stackrel {\mathrm {def} }{=}}\ \gamma ^{\mu }A_{\mu }}$.