Discovery of concealed symmetries in materials through experimental or theoretical analysis.Hidden symmetry revelation concerns the discovery of symmetries in physical systems that are not immediately apparent from their observed properties or governing equations. A symmetry is a transformation that leaves a system unchanged; when hidden, it may only emerge under specific conditions, such as at certain energy scales, in particular phases of matter, or through careful theoretical analysis. The seed definition mentions materials, but the concept extends to particle physics, cosmology, and condensed matter. Uncovering such symmetries often leads to deeper understanding, new conservation laws, and predictions of novel phenomena.
Hidden symmetries are typically revealed through mathematical analysis of a system's equations or through experimental probes that access regimes where the symmetry becomes manifest. For example, in condensed matter, a material might appear disordered, but a transformation of its electronic wavefunctions could reveal an underlying order. In particle physics, symmetries like supersymmetry are proposed to be broken at low energies but restored at high energies, requiring colliders to probe. The process involves identifying invariants, mapping the system to a simpler equivalent form, or finding that certain observables remain constant under transformations that were previously overlooked.
Revealing hidden symmetries can lead to the design of materials with exotic properties, such as topological insulators, and to the prediction of new particles in high-energy physics.
| a_{X-Y} | variable | mass-scaled anomaly difference — anomaly difference |
| a_X | variable | anomaly of particle X — anomaly |
| a_Y | variable | anomaly of particle Y — anomaly |
| m_X | variable | mass of particle X — mass kilogram |
| m_Y | variable | mass of particle Y — mass kilogram |
| s | variable | sigmoid function value — sigmoid function |
| ζ | variable | input argument — argument |
| a | variable | steepness parameter — steepness parameter |
| exp | operator | raises e to the given power — exponential function |
