7 problems

In relativistic particle physics, approximate symmetries may be observed even when the underlying theory has an exact symmetry. Nambu's conjecture. Some of the approximate symmetri…

Long-range interacting systems exhibit spontaneous symmetry breaking, with collective fluctuation modes whose frequencies remain nonzero as the wave number tends to zero. The relev…

Let $L$ denote the system size, and let the ground state be obtained through the double limit in equation … resembles, or coincides with, the large $L$ limit of…

Consider a quantum lattice system with a continuous symmetry whose unique ground state exhibits long-range order but no spontaneous symmetry breaking. Suppose that the low-lying ex…

Let $G=SO(3)$, and let $(\omega_\beta)$ be the infinite-volume equilibrium states obtained as weak limits of the finite-volume states for the Heisenberg ferromagnet (or its antifer…

Let the Abelian gauge symmetry undergo the discrete breaking … Let $\gamma_h$, with $\gamma_h\in U(1)$, denote the automorphisms acting on the field-operator algebra $\cal F$, and…

Consider the lattice variational principle with the action and constraints specified in the paper, and let the lattice contain many sites and the system contain many particles. Dis…