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While it has always been my argument that many aspect of the lessons we learn out of condensed matter physics can be fundamental and applicable to a wide range of physics field, I also think that it needs to be applied or referred to accurately.
This is not quite correct. While the symmetry of the crystal structure can certainly be a factor in determining the phonon spectrum, it isn't the the only one, and it isn't uniquely determined by it. The form factor of the crystal structure is also one crucial aspect. That's why you can have 2 bcc lattices with the same lattice atoms, but you can easily have different basis at each of the lattice points and thus, different form factors, which in turn changes the phonon spectrum.
I'm sure this isn't a crucial mistake. , Still, since you are mentioning the "crystal structure" rather than the reciprocal lattice structure, silicon is an FCC diamond crystal, not bcc.
A "massive phonon" is a rather strange term. In the heavy fermion system, there are no "massive phonons". Rather, the renormalization is due to several many-body interactions, possibly even the spin-fluctuation interactions. This is certainly confirmed by the fact that there are many systems that share the same crystal structure as the heavy fermion system. Yet, those other systems do not have the same heavy fermions. So if what you mentioned earlier that the phonon spectrum is only dependent on the crystal lattice, this observation would be inconsistent to that claim.
Zz.
Lawrence B. Crowell said:The symmetry of the lattice determines the spectra of phonons in much the same way that a symmetry group in particle physics determines the structure or states of elementary particles. The particle states are given by eigenstates of Bloch waves on a lattice, which in lattice QCD are analogously seen in Mantin periodic Lagrangians.
This is not quite correct. While the symmetry of the crystal structure can certainly be a factor in determining the phonon spectrum, it isn't the the only one, and it isn't uniquely determined by it. The form factor of the crystal structure is also one crucial aspect. That's why you can have 2 bcc lattices with the same lattice atoms, but you can easily have different basis at each of the lattice points and thus, different form factors, which in turn changes the phonon spectrum.
If small spheres are assigned to these points the lattice is a body centered cubic lattice (bcc), where the bcc in three dimensions is the crystalline lattice of silicon.
I'm sure this isn't a crucial mistake. , Still, since you are mentioning the "crystal structure" rather than the reciprocal lattice structure, silicon is an FCC diamond crystal, not bcc.
In this way the mass of the gauge particle (analogous to a massive phonon) is renormalized in much the same way massive particles have renormalized masses in a Brillouin zones.
A "massive phonon" is a rather strange term. In the heavy fermion system, there are no "massive phonons". Rather, the renormalization is due to several many-body interactions, possibly even the spin-fluctuation interactions. This is certainly confirmed by the fact that there are many systems that share the same crystal structure as the heavy fermion system. Yet, those other systems do not have the same heavy fermions. So if what you mentioned earlier that the phonon spectrum is only dependent on the crystal lattice, this observation would be inconsistent to that claim.
Zz.