In quantum theory, symmetries act on states and operators through unitary or antiunitary transformations. Continuous symmetries generate conserved currents, while discrete symmetries such as parity, charge conjugation, and time reversal impose additional constraints on observables and allowed interactions.

When the equations of motion are symmetric but the vacuum is not, the system exhibits spontaneous symmetry breaking. The vacuum manifold may contain degenerate minima, and massless Goldstone modes appear for broken continuous global symmetries, with important exceptions and modifications in gauge theories.

Anomalies arise when a symmetry of the classical action fails after regularization and quantization. Gauge anomalies are especially dangerous because they can destroy consistency, whereas some global anomalies encode physically meaningful selection rules and transport phenomena.

Ward identities express the consequences of symmetry at the level of correlation functions and scattering amplitudes. They are indispensable in proving renormalization constraints, consistency of gauge theories, and relations among Green's functions. In advanced settings, current algebra can reveal nonperturbative information about the spectrum and operator product structure.