Physical meaning of the Feynman slash

  • #1
The Feynman slash

[tex]\slashed{a}=\gamma^\mu a_\mu[/tex]

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?
 

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  • #2
marcus
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The Feynman slash

[tex]\slashed{a}=\gamma^\mu a_\mu[/tex]

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
 
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  • #3
marcus
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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?
 

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