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The correspondance between symmetries and conserved quantities is apparent through conservation laws. Much work has been done, especially in quantum physics, to relate every conserved quantity to some symmetry. One such quantity that still defies all such attempts is mass. Some other examples include:

• Acceleration is invariant under the Galilean transformations.
• The speed of light invariant under the Lorentz transformations of special relativity.
• time invariance makes energy a conserved quantity, hence an invariant.
• translational invariance implies that momentum is conserved.
• rotational invariance implies that angular momentum is conserved.

See also:

• covariantIn category theory, see covariant functor. In tensor analysis, a covariant coordinate system is reciprocal to a corresponding contravariant coordinate system. Roughly speaking, a covariant tensor is a vector field that defines the topology of a space; it, contravariantContravariant is a mathematical term with a precise definition in tensor analysis. It specifies precisely the method (direction of projection) used to derive the components by projecting the magnitude of the tensor quantity onto the coordinate system bein
• principle of relativityIn general, the principle of relativity is the requirement that the laws of physics be the same for all observers. Somewhat more particularly, the measurements an observer makes in his frame of reference of an important event are related in a particular w