 Kaluza–Klein theory

Kaluza-Klein theory obtains lower-dimensional fields from a higher-dimensional metric and other fields on compact dimensions. In the displayed fixed-radius circle ansatz, the off-diagonal metric supplies a vector. The coordinate change $y\mapsto y+\lambda (x)$ is compensated by $A\mapsto A-d\lambda$, producing an Abelian gauge symmetry. Allowing the radius to vary adds a scalar modulus. Kaluza-Klein modes also include nonzero internal momenta, giving a tower of massive fields.

// Target: quantum-field-theory.bigb

Kaluza-Klein theory is a theoretical framework that attempts to unify gravity and electromagnetism by extending the concept of spacetime to include extra dimensions. It originated from the work of Theodor Kaluza and Oskar Klein in the early 20th century. The key idea is as follows: 1. **Extra Dimensions**: Kaluza proposed that, in addition to the familiar three spatial dimensions and one time dimension, there exists a fifth dimension.