Symmetry and Noether Theorem for Brain Microcircuits

Symmetry as a feature of beauty and harmony is a concept that emerged in ancient times during the Greek and Roman antiquity. In contrast, the modern concept of symmetry refers to the properties of a geometrical object or a physical system that preserves the same form features when subjected to a specific group of transformations defined by mathematical operations, e.g., reflection, rotation, translation. While the applications of symmetry range from physics to computational neuroscience, this chapter will deal with how brain function in the normal and pathological state can be understood as a result of symmetry breaking (SB).