Nambu-Goldstone modes appear when a continuous symmetry is spontaneously broken.

Generally, the correspondence between continuous symmetries and conservation laws is given by Noether's theorem.

A common example is crystalline solids, which break continuous translational symmetry.

The search for continuous symmetries only intensified with the further developments of quantum field theory.

More abstractly, a charge is any generator of a continuous symmetry of the physical system under study.

In it are discussed continuous symmetries opposed to, for example, discrete symmetries.

Mathematically, continuous symmetries are described by continuous or smooth functions.

A continuous broken symmetry leads to a Goldstone boson.

In particular, dissipative systems with continuous symmetries need not have a corresponding conservation law.

And suppose that the integral is invariant under a continuous symmetry.