Phonons vs Gauge Bosons: What's the Difference?

[nuby]

Whats the difference between phonons and gauge bosons?

 

[olgranpappy]

Whats the difference between phonons and gauge bosons?

In classical field theory the Lagrangian of interest (which basically defines what "theory" I'm talking about) may have a symmetry. For example, it may happen that my Lagrangian doesn't change if I multiply the fields by a phase $e^{i\phi}$. If I let $\phi$ depend on space and time (this is called "gauging") then the multiplication of the fields by $e^{i\phi(x)}$ no longer leaves the Lagrangian invariant. But, by introducing *more* fields called gauge fields (i.e., by changing the Lagrangian I start with, changing the theory), I can force the Lagrangian to be invariant. When I quantize the gauge fields, the resulting particles are called "gauge bosons".

When I quantize the theory of lattice vibrations, I end of with particles (which are bosons) called "phonons".