In Feynman slash notation, a slashed vector contracts with what matrices?

In Feynman slash notation, a slashed vector contracts with gamma matrices. For a four-vector A, the notation is defined as A̸ = γ^μA_μ, with the repeated index summed over spacetime components.

The gamma matrices encode the geometry of special relativity in Dirac’s theory of spin-½ particles. They obey anticommutation relations involving the Minkowski metric, allowing expressions involving four-vectors to be handled compactly as matrices acting on spinors.

A common mix-up is with Pauli matrices. Pauli matrices appear inside common representations of the spatial gamma matrices, but they are not the matrices being contracted in the definition itself. Gell-Mann matrices belong mainly to the color-symmetry mathematics of quantum chromodynamics, while Hadamard matrices are associated with other areas of mathematics and computing.

Slash notation is especially useful for four-momentum and derivatives: p̸ = γ^μp_μ and ∂̸ = γ^μ∂_μ. It turns the Dirac equation into the compact form (i∂̸ − m)ψ = 0.