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There are two other representations for matter. One is an assignment of charges to quarks and leptons; these are called color representations. The other is an assignment of charges to "fractions of a fermion" or an assignment of a number to each of two or more particles more or less equally. This representation is called the masses representations. Of the two, the masses are the more useful for actual calculations while the color representations remain useful for calculating the interaction strengths (which are given as matrix elements in terms of matrix elements of the group generators, which are usually given in terms of Clebsch-Gordan coefficients).

Note, however, that it is possible to make matter in the most abstract sense by combining two antiparticles (in this case the antiproton and the positron) into a single matter particle (see positronium). Thus, the most general matter of the Standard Model is actually a self-absorbed matrix representation of the group SU(3)C x SU(2)L, as discussed at the end of the secondary school curriculum.

Since the antihermitic property is in all possible combinations of the two - the combination of two anti-parity right-handed particles and the combination of two left-handed ones - the space of the antihermitic property is also a representation of the product group SU(3,C) x SU(2)L x U(1).

Just as for the hermitic property, it is possible to omit certain physical quantities from the representation. Thus, it is possible to omit the antihermitic property of quarks and leptons, and it is even possible to omit the either left- or right-handed properties of a particle when they are ignored in the interaction. It is also possible to ignore the U(1) charge. In a very broad sense it is therefore possible to omit charge, color, and antisymmetry, and still form a consistent representation. In a similar vein, for other charge assignments, both conserved and violated (right- and left-handed) properties, such as baryon number or lepton number, can be omitted to some degree of accuracy as well. d2c66b5586