  We extend the framework of analyzing the 2HDM in its orbit space to study the
one-loop effective potential before and after electroweak symmetry breaking. In
this framework, we present a comprehensive analysis of global symmetries of the
one-loop thermal effective potential in the 2HDM, demonstrating when the global
symmetries of the tree-level 2HDM potential are broken by loop contributions.
By introducing light-cone coordinates and generalizing the bilinear notation
around the vacuum, we present a geometric view of the scalar mass matrix and
on-shell renormalization conditions.
