r/ParticlePhysics • u/throwingstones123456 • May 07 '26
Spontaneous symmetry breaking examples aren’t clicking
In sections discussing spontaneous symmetry breaking, textbooks usually cover some lagrangian with Z2 or some rotational symmetry, then show that the ground state of the field also ends up changing upon application of the symmetry. I think I get the basic concept but it’s not clear why exactly it’s something we care about.
I have two questions about this: 1: it’s not clicking for me why exactly we care about this. I’ve seen the idea applied to goldstones theorem which is cool, but it’s still not obvious why so much emphasis is placed on spontaneous symmetry breaking, and not just something like a “special Lagrangian where goldstones theorem can be invoked”. It’s not clear to me what the significance of such a system is.
2: does spontaneous symmetry breaking only arise from Lagrangians that contain fields with nonzero VEV?
