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Concept
Isospin
Summary
In nuclear physics and particle physics, isospin (I) is a quantum number related to the up- and down quark content of the particle. More specifically, isospin symmetry is a subset of the flavour symmetry seen more broadly in the interactions of baryons and mesons.
The name of the concept contains the term spin because its quantum mechanical description is mathematically similar to that of angular momentum (in particular, in the way it couples; for example, a proton–neutron pair can be coupled either in a state of total isospin 1 or in one of 0). But unlike angular momentum, it is a dimensionless quantity and is not actually any type of spin.
Etymologically, the term was derived from isotopic spin, a confusing term to which nuclear physicists prefer isobaric spin, which is more precise in meaning. Before the concept of quarks was introduced, particles that are affected equally by the strong force but had different charges (e.g. protons and neutrons) were considered different states of the same particle, but having isospin values related to the number of charge states. A close examination of isospin symmetry ultimately led directly to the discovery and understanding of quarks and to the development of Yang–Mills theory. Isospin symmetry remains an important concept in particle physics.
In the modern formulation, isospin (I) is defined as a vector quantity in which up and down quarks have a value of I = 1/2, with the 3rd-component (I3) being +1/2 for up quarks, and −1/2 for down quarks, while all other quarks have I = 0. Therefore, for hadrons in general, where nu and nd are the numbers of up and down quarks respectively,
In any combination of quarks, the 3rd component of the isospin vector (I3) could either be aligned between a pair of quarks, or face the opposite direction, giving different possible values for total isospin for any combination of quark flavours. Hadrons with the same quark content but different total isospin can be distinguished experimentally, verifying that flavour is actually a vector quantity, not a scalar (up vs down simply being a projection in the quantum mechanical z axis of flavour space).
Official source
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