non-linear sigma model

A non-linear sigma model is a theoretical framework in physics used to describe how certain fields, representing particles or other entities, change or "move" within curved spaces called manifolds. Unlike linear models where changes are straightforward, non-linear sigma models account for complex, curved relationships, making them useful for understanding phenomena like phase transitions or quantum fields with internal symmetries. They connect geometry and physics by examining how fields map from spacetime into these curved target spaces, providing insights into the underlying structure and interactions of fundamental particles or systems with symmetry properties.