However, line groups may have more than one dimension, and they may involve those dimensions in its isometries or symmetry transformations.

Isospin is the symmetry transformation of the weak interactions.

The functional measure would have to be invariant under the one parameter group of symmetry transformation as well.

All multiplicative quantum numbers belong to a symmetry (like parity) in which applying the symmetry transformation twice is equivalent to doing nothing.

A symmetry transformation between the two is called parity.

Identification of the remaining odd parts of these functions was formulated based on symmetry transformations that interrelate domains.

Monodromy defects are created by twisting the boundary condition along a cut by a symmetry transformation.

These are the defining symmetry transformations of General Relativity since the theory is formulated only in terms of a differentiable manifold.

These are capable of changing the physical field strengths and are therefore no proper symmetry transformations.

Either the dipole moment stays invariant under the symmetry transformation ("1") or it changes its direction ("-1"):