Physical meaning of the Feynman slash

[FredMadison]

The Feynman slash

$$\slashed{a}=\gamma^\mu a_\mu$$

maps a four-vector a to its Clifford algebra-representation. This is a linear combination of the gamma matrices with the components of a acting as expansion coefficients. What physical significance does this new object have?

The gamma matrices are used in the Dirac equation to take the formal square-root of the D'Alembertian operator. So can one interpret the slashed a as a formal square-root of a^2?

 

[marcus]

The Feynman slash

$$\slashed{a}=\gamma^\mu a_\mu$$

maps a four-vector a to its Clifford algebra-representation. This is a linear combination of the gamma matrices with the components of a acting as expansion coefficients. What physical significance does this new object have?

The gamma matrices are used in the Dirac equation to take the formal square-root of the D'Alembertian operator. So can one interpret the slashed a as a formal square-root of a^2?

I can't tell you the physical significance but the notation is evidently very convenient in quantum field theory and is used a lot. It allows equations to be written in more compact form. I looked up "feynman slash" in wikipedia and it gave a lot of examples and identities.
http://en.wikipedia.org/wiki/Feynman_slash_notation

 

[marcus]

Feynman slash plays a central role in this approach to merging quantum gravity and the Standard Model particle theory, by Chamseddine Connes and Mukhanov
http://arxiv.org/abs/1411.0977

Apparently our LaTex version used to support the " \slashed " command, but I think it may no longer do so. Maybe there is now a different command?