Euclidean conformal transformation

A Euclidean conformal transformation pulls the flat metric back to a position-dependent positive multiple of itself. Its infinitesimal generator obeys the conformal Killing equation.

In $d$ flat dimensions, an infinitesimal conformal transformation generated by ${ϵ}^{\mu }$ satisfies ${\partial }_{\mu }{ϵ}_{\nu }+{\partial }_{\nu }{ϵ}_{\mu }=2(\partial \cdot ϵ){\delta }_{\mu \nu }/d$.