Identical particles fermions, which do not share quantum states as described by the Pauli exclusion principle. Examples of bosons are photons, gluons, phonons, helium-4 nuclei and all mesons. Examples of fermions are electrons, neutrinos, quarks, protons, neutrons, and helium-3 nuclei. The fact that particles can be identical has important consequences in statistical mechanics. Calculations in statistical mechanics rely on probabilistic arguments, which are sensitive to whether or not the objects being studied are identical. As a result, identical particles exhibit markedly different statistical behaviour from distinguishable particles. For example, the indistinguishability of particles has been proposed as a solution to Gibbs' mixing
Chirality (physics) to begin with, and therefore the pions are not massless, but have small masses: they are pseudo-Goldstone bosons. For more "light" quark species, flavors in general, the corresponding chiral symmetries are "U(N)×U(N)", decomposing into and exhibiting a very analogous chiral symmetry breaking pattern. Most usually, = 3 is taken, the "u, d", and "s" quarks taken to be light (the Eightfold way (physics)), so then approximately massless for the symmetry to be meaningful to a lowest order, while the other three quarks are sufficiently heavy to barely have a residual chiral symmetry be visible for practical purposes. In theoretical physics,