Isospin
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Template:Flavour quantum numbers
Isospin (isotopic spin, isobaric spin) is a physical quantity which is mathematically analogous to spin. Isospin was introduced by Werner Heisenberg to explain the fact that the strength of the strong interaction is almost the same between two protons or two neutrons as between a proton and a neutron, unlike the electromagnetic interaction which depends on the electric charge of the interacting particles. Heisenberg's idea was that protons and neutrons were essentially two states of the same particle, the nucleon, analogous to the 'up' and 'down' states of a spin-1/2 particle. The proton, for example, was analogous to the 'spin-up' state and the neutron to the 'spin-down' state. Even if one ignores charge, the proton and neutron are still not completely symmetric, the neutron is slightly more massive, and so isospin is not a perfect symmetry of the strong force.
Isospin infinitesimal generators transform as the three-dimensional adjoint representation of SU(2). The generators of isospin are described by Pauli matrices. In the original formulation of Yang-Mills theory, protons and neutrons were described as two components of an isospin doublet, belonging to the fundamental representation of SU(2), and interacting by means of pions, which were taken to be the SU(2) gauge bosons.
In the framework of the Standard Model, isospin invariance of the strong interaction is a result of the fact that particles differing only in the replacement of an up quark for a down quark (such as protons (uud) and neutrons (udd)) behave the same, since strong interactions are independent of the flavor of particles. Thus, isospin invariance appears as a consequence of the flavor invariance of strong interactions. Isospin invariance is absent in electromagnetic and weak interactions since they do depend on quark flavour.