Backrowena: Spontaneous Symmetry Breaking
Thermodynamics & Statistical Physics arc, page 67 of 193. Back to The Pixelated Physics Universe
Who they are
Backrowena has one line, and says it often: “Symmetric room. everyone in the back.”
Backrowena is a character of the Thermodynamics & Statistical Physics arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Spontaneous symmetry breaking: the ground state lacks the symmetry of the Hamiltonian.
$$ \begin{gathered} V(\phi) = -\mu^{2}|\phi|^{2} + \lambda |\phi|^{4} \\ |\phi_0|^{2} = \frac{\mu^{2}}{2\lambda} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $V(\phi)$ | potential energy density of the field | — |
| $\phi$ | complex scalar field | — |
| $\mu^{2}$ | mass parameter (positive here) | — |
| $\lambda$ | self-coupling | — |
| $\phi_0$ | vacuum (ground-state) value of the field | — |
Sources
Crossovers
Backrowena meets Avergail (Mean Field Theory). Backrowena's ground state breaks the symmetry of the Hamiltonian. Avergail's mean-field theory is the simplest place to see it: below the critical temperature, the averaged field picks one direction.
Backrowena meets Vortia & Antivortia (BKT Transition). Backrowena says symmetric laws can have an asymmetric ground state. Vortia and Antivortia say that in two dimensions, a continuous symmetry cannot be broken at any non-zero temperature, yet a BKT transition still happens, through bound vortex pairs coming unbound.
Backrowena meets Glueba (Yang–Mills and the Mass Gap). Backrowena's symmetry breaking gives gauge bosons mass in the electroweak theory, by way of the Higgs field. Glueba's mass gap would have to come from somewhere else: pure Yang–Mills has no Higgs, and proving its gap is an unsolved problem.
Wear the lore
Concept keywords: Spontaneous Symmetry Breaking, Backrowena, Thermodynamics & Statistical Physics, physics lore, Pixelated Physics