I am not the one trying to re-define continuous symmetries of the Lagrangians of physical theories. I think you should better understand the thread's use of symmetry in the OP before trying to insert an unrelated definition.
Yes, I see what you mean in that 'symmetry' for mathematicians... ...is a very different concept to what is observed physically. Hence as I began to become aware of it I had to change the physical description to 'handedness'. The important point now of course is that handedness is rather difficult to model mathematically - and seems to be left out of much physical thinking which tries to reduce subatomic particles to pointlike entities controlled by probability waves. FOLZONI
