Special conformal transformation
Encyclopedia
In mathematics, a special conformal transformation is a member of the conformal symmetry group
. It is given by
Its infinitesimal generator
is
Such a transformation can also be written as sequence of an inversion (xμ → xμ/x2), a translation
(xμ → xμ − bμ), and an inversion:
Conformal symmetry
In theoretical physics, conformal symmetry is a symmetry under dilatation and under the special conformal transformations...
. It is given by
Its infinitesimal generator
Generating set of a group
In abstract algebra, a generating set of a group is a subset that is not contained in any proper subgroup of the group. Equivalently, a generating set of a group is a subset such that every element of the group can be expressed as the combination of finitely many elements of the subset and their...
is
Such a transformation can also be written as sequence of an inversion (xμ → xμ/x2), a translation
Translation (physics)
In physics, translation is movement that changes the position of an object, as opposed to rotation. For example, according to Whittaker:...
(xμ → xμ − bμ), and an inversion: