See: Symmetry, Analytic symmetry, Duality, Physics

Gain intuition from gauge theory about Lie theory, symmetry, physics.

• What is the gauge theory that relates the symmetry in counting forwards and backwards?
• What is the gauge theory for the symmetry that the derivative of {$e^x$} is {$e^x$}?
• Understand how the gauge theory of electrodynamics (classical and/or quantum?) explains how particles emit photons to go from higher energy states to lower energy states.
• What is self-energy? Is it related to the way that a particle may affect itself by way of its interactions with a field? Is the latter related to gauge theory?
• Why does the Yang-Mills theory work?
• Are the doubts and counterquestions related to electromagnetism, U(1) and the related gauge theory?
• In what sense does gauge theory express the slack in the way that holistic divisions (0,1,2,3) and lax divisions (7,6,5,4) complement each other? And does that relate to the four forces? And is it expressed by the equations 3+3=6, 4+3=7, 5+3=0, 6+3=1 ?