Gluon field tensor
In theoretical particle physics, the gluon field strength tensor is a second order tensor field characterizing the gluon interaction between quarks.
The strong interaction is one of the fundamental interactions of nature, and the quantum field theory (QFT) to describe it is called quantum chromodynamics (QCD). Quarks interact with each other by the strong force due to their color charge, mediated by gluons. Gluons themselves possess color charge and can mutually interact.
The gluon field strength tensor is a rank 2 tensor field on the spacetime with values in the adjoint bundle of the chromodynamical SU(3) gauge group (see vector bundle for necessary definitions). Throughout, Latin indices (typically a, b, c, n) take values 1, 2, ..., 8 for the eight gluon color charges, while Greek indices (typically α, β, μ, ν) take values 0 for timelike components and 1, 2, 3 for spacelike components of four-vectors and four-dimensional spacetime tensors. Throughout all equations, the summation convention is used on all color and tensor indices, unless explicitly stated there is no sum to be taken.
Below the definitions (and most of the notation) follow K. Yagi, T. Hatsuda, Y. Miake and Greiner, Schäfer.
The tensor is denoted G, (or F, F, or some variant), and has components defined proportional to the commutator of the quark covariant derivative Dμ:
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