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
Gauge theory Lagrangian. In the quantized version of the obtained classical field theory, the quanta of the gauge field "A"("x") are called gauge bosons. The interpretation of the interaction Lagrangian in quantum field theory is of scalar bosons interacting by the exchange of these gauge bosons. The picture of a classical gauge theory developed in the previous section is almost complete, except for the fact that to define the covariant derivatives "D", one needs to know the value of the gauge field formula_29 at all space-time points. Instead of manually specifying the values of this field, it can be given as the