Yang-Mills Lagrangian (${\mathcal{L}}_{\mathrm{YM}}=-F_{\mu \nu }^a{F}^{a\mu \nu }/4$)

In a Minkowski-space convention with metric $(+---)$ and canonically normalized gauge fields, the displayed Lagrangian density supplies their kinetic term. The Yang-Mills field strength contains a quadratic gauge-potential term, which generates cubic and quartic Yang-Mills self-interactions when the field-strength square is expanded. The coupling can instead be placed as an overall prefactor by rescaling the gauge potential; the normalization convention must be fixed before comparing coefficients.