Invariance and Conservation Principles
Two important aspects in physics are the invariance (or symmetry) of the equations describing the behavior of a system under a given transformation (for example, a translation of the system frame) and the conservation of some physical quantities (e.g., the momentum). The invariance properties are abstract features of the mathematical formalism. These invariance properties are intimately connected to conservation laws. For example, the conservation of angular momentum is related to the invariance under spatial rotations; the conservation of the linear momentum is related to the homogeneity of space. Noether’s theorem formally expresses the fact that a physical conserved quantity corresponds to each invariant, and vice versa.