spinnor

A spinor is a mathematical object that transforms in a specific way under rotations and boosts in spacetime. It is a generalization of the concept of a vector, which transforms linearly under these transformations. Spinors are fundamental in the study of quantum mechanics and quantum field theory, particularly in the context of the Dirac equation and the Standard Model of particle physics.

In three-dimensional Euclidean space, spinors can be thought of as complex numbers that transform according to a specific representation of the rotation group SO(3). In four-dimensional Minkowski spacetime, spinors transform according to the Lorentz group SO(3,1). There are two types of spinors in four-dimensional spacetime: Weyl spinors and Dirac spinors. Weyl spinors are two-component spinors that transform according to the spin-1/2 representation of the Lorentz group, while Dirac spinors are four-component spinors that transform according to the spin-1/2 representation of the Lorentz group and its conjugate.

Spinors play a crucial role in the description of particles with half-integer spin, such as fermions. They are also used in the study of topological phases of matter and in the formulation of string theory. The concept of spinors was first introduced by Elie Cartan in the early 20th century and has since become an essential tool in modern theoretical physics.