In one of my papers titled "Lorentz Violation and Condensed Matter Physics" I pointed out several operators in condensed matter physics that arise from Lorentz violation in the Standard Model Extension. The coefficients of these operators employed in condensed matter physics are clearly enhanced, as shown from different references in the paper.
I have a feeling that we are missing something very fundamental in our understanding of Lorentz symmetry. At the heart, it makes complete sense and it is important that physics remains the same independent of the frame of reference, but one subtle point about the principle of relativity is that it is formulated for the vacuum. What if we perform a Lorentz transformation and end up in a condensed matter system where the speed of light can be slower, the mass of the electron can be different? The physics has clearly changed to some extent. This might be the reason we see an enhanced value of the coefficients of Lorentz violating operators in condensed matter.
[1] https://arxiv.org/abs/1403.7622
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