discovered by a particle accelerator group at Brookhaven. Gell-Mann received the 1969 Nobel Prize in Physics for his work on the theory of elementary particles. Historical development Development Historically, quarks were motivated by an understanding of flavour symmetry. First, it was noticed (1961) that groups of particles were related to each other in a way that matched the representation theory of SU(3). From that, it was inferred that there is an approximate symmetry of the universe which is parametrized by the group SU(3). Finally (1964), this led to the discovery of three light quarks (up, down, and strange) interchanged by these SU(3) transformations. Modern interpretation The eightfold way may be understood in modern terms as a consequence of flavor symmetries between various kinds of quarks. Since the strong nuclear force affects quarks the same way regardless of their flavor, replacing one flavor of quark with another in a hadron should not alter its mass very much, provided the respective quark masses are smaller than the strong interaction scale—which holds for the three light quarks. Mathematically, this replacement may be described by elements of the SU(3) group. The octets and other hadron arrangements are representations of this group. Flavor symmetry SU(3) There is an abstract three-dimensional vector space: and the laws of physics are approximately invariant under applying a determinant-1 unitary transformation to this space (sometimes called a flavour rotation): Here, SU(3) refers to the Lie group of 3×3 unitary matrices with determinant 1 (special unitary group). For example, the flavour rotation is a transformation that simultaneously turns all the up quarks in the universe into down quarks and vice versa. More specifically, these flavour rotations are exact symmetries if only strong force interactions are looked at, but they are not truly exact symmetries of the universe because the three quarks have different masses and different electroweak interactions. This approximate symmetry is called flavour symmetry, or more specifically flavour SU(3) symmetry. Connection to representation theory Assume we have a certain particle—for example, a proton—in a quantum state . If we apply one of the flavour rotations A to our particle, it enters a new quantum state which we can call . Depending on A, this new state might be a proton, or a neutron, or a superposition of a proton and a neutron, or various other possibilities. The set of all possible quantum states spans a vector space. Representation theory is