Gluon field
Throughout this article, Latin indices take values 1, 2, ..., 8 for the eight gluon color charges, while Greek indices take values 0 for timelike components and 1, 2, 3 for spacelike components of four-dimensional vectors and tensors in spacetime.Throughout all equations, the summation convention is used on all color and tensor indices, unless explicitly stated otherwise.The components which act on the color triplet quark fields are given by: wherein i is the imaginary unit, and is the dimensionless coupling constant for QCD, andThe partial derivative term includes a 3 × 3 identity matrix, conventionally not written for simplicity.which leaves the gluon field strength tensor unchanged is;[3] where is a 3 × 3 matrix constructed from the tn matrices above and θn = θn(r, t) are eight gauge functions dependent on spatial position r and time t. Matrix exponentiation is used in the transformation.