symmetrybroken

Symmetrybroken is a term used to describe systems or states in which a symmetry of the governing laws is not reflected in the observed configuration. In physics, many laws are invariant under certain transformations, but the actual state of a system can select a specific orientation or structure, thereby breaking that symmetry. When the symmetry is still present in the equations but not in the state, the situation is often described as spontaneous symmetry breaking. If the symmetry is explicitly violated by a term in the equations, the breaking is explicit rather than spontaneous.

There are several forms of symmetry breaking. Spontaneous symmetry breaking occurs when the system’s lowest-energy state (the ground state) is not invariant under the full symmetry, even though the underlying laws are. This often involves an order parameter that acquires a nonzero value, and it can lead to degenerate ground states and the emergence of collective excitations, such as Goldstone bosons in continuous-symmetry cases. Explicit symmetry breaking arises when a term in the theory breaks the symmetry directly, without requiring a special state. Dynamical symmetry breaking refers to breaking induced by interactions and dynamics rather than by a static term alone; in quantum field theory this is closely related to mechanisms like confinement or the Higgs mechanism.

Common examples span physics and materials science. Ferromagnets break rotational symmetry below the Curie point; crystals break continuous translational and rotational symmetries to a discrete lattice; the Ising model breaks Z2 symmetry; in particle physics, the Higgs mechanism involves spontaneous breaking of gauge symmetry, giving mass to gauge bosons.

In mathematical terms, symmetrybreaking can be described by a symmetry group G acting on a state space, with the broken phase corresponding to a subgroup H and a vacuum manifold G/H.