The color singlet state is:  In other words, if one could measure the color of the state, there would be equal probabilities of it being red-antired, blue-antiblue, or green-antigreen. There are eight remaining independent color states, which correspond to the "eight types" or "eight colors" of gluons. Because states can be mixed together as discussed above, there are many ways of presenting these states, which are known as the "color octet". One commonly used list is:  These are equivalent to the Gell-Mann matrices. The critical feature of these particular eight states is that they are linearly independent, and also independent of the singlet state, hence 32 − 1 or 23. There is no way to add any combination of these states to produce any other, and it is also impossible to add them to make r, g, or b the forbidden singlet state. There are many other possible choices, but all are mathematically equivalent, at least equally complicated, and give the same physical results. Technically, QCD is a gauge theory with SU(3) gauge symmetry. Quarks are introduced as spinors in "N"f flavors, each in the fundamental representation (triplet, denoted 3) of the color gauge group, SU(3). The gluons are vectors in the adjoint representation (octets, denoted 8) of color SU(3). For a general gauge group, the number of force-carriers (like photons or gluons) is always equal to the dimension of the adjoint representation. For the simple case of SU("N"), the dimension of this representation is . In terms of group theory, the assertion that there are no color singlet gluons is simply the statement that quantum chromodynamics has an SU(3) rather than a U(3) symmetry. There is no known "a priori" reason for one group to be preferred over the other, but as discussed above, the experimental evidence supports SU(3). The U(1) group for electromagnetic field combines with a slightly more complicated group known as SU(2) – S stands for "special" – which means the corresponding matrices have determinant +1 in addition to being unitary. Since gluons themselves carry color charge, they participate in strong interactions. These gluon-gluon interactions constrain color fields to string-like objects called "flux tubes", which exert constant force when stretched.