Symmetryallowed

Symmetryallowed is a descriptor used in mathematics, physics, and related disciplines to indicate that a particular operation, transformation, or arrangement is compatible with the symmetry of a system. When something is symmetryallowed, it preserves or respects invariance under the system's symmetry group.

In group theory, an operation is symmetryallowed if it commutes with the action of the symmetry group on the objects in question. Such operations map symmetry-equivalent configurations to other symmetry-equivalent configurations, maintaining invariant properties across the group orbit.

In physics and chemistry, symmetryallowed often appears in the context of selection rules and transitions. A matrix element or transition is symmetryallowed if the direct product of the representations involved contains the trivial representation, allowing a nonzero probability amplitude. This concept governs which spectral lines or transitions are allowed.

In computation and data analysis, symmetryallowed can refer to algorithms or models that preserve symmetry properties of the input data, ensuring consistent outputs under symmetry transformations. Examples include symmetry-preserving neural networks and invariant feature extraction methods.

The term is not a formal, widely standardized label, but a descriptive one used across disciplines to contrast symmetryallowed operations with symmetryforbidden ones. Related terms include symmetry-permitted, symmetry-compliant, and invariant under symmetry.