What is the difference between a spinor and a vector?

Spinors transform in a single-sided way. Geometrically, vectors are the oriented lines that you’re used to, with a weight equal to the vector’s magnitude. Spinors represent linear combinations of scalars and bivectors, oriented planes.

What is a spinor quantum mechanics?

In geometry and physics, spinors /spɪnər/ are elements of a complex vector space that can be associated with Euclidean space. Like geometric vectors and more general tensors, spinors transform linearly when the Euclidean space is subjected to a slight (infinitesimal) rotation.

Is a spinor a tensor?

Then, in the language used in this context, a “tensor” is an element of some tensor product space formed from M and its dual space, while a “spinor” is an element of some tensor product space formed from S and its complex conjugate space ˉS and their dual spaces.

Is a spinor a vector?

Spinor is a vector in the basis of not space-time, but its spin states; in on sense, spinor is not a vector, since it will not transform as you transform the space (rotation, etc) .

What is Pauli spinor?

Spinors of the Pauli spin matrices The Pauli matrices are a vector of three 2×2 matrices that are used as spin operators. Given a unit vector in 3 dimensions, for example (a, b, c), one takes a dot product with the Pauli spin matrices to obtain a spin matrix for spin in the direction of the unit vector.

How many components does a spinor have?

In quantum field theory I’ve learned that a spinor is a 4 component complex vector field on Minkowski space which transforms under the chiral representation of the Lorentz group.

Do the Pauli matrices commute?

Pauli vectorEdit Note that in this vector dotted with Pauli vector operation the Pauli matrices are treated in a scalar like fashion, commuting with the vector basis elements.

Is electron a spinor?

An electron is known as a Dirac spinor. So a free electron moving in space that had left helicity with linear momentum and spin pointing in opposite directions may end up having a right helicity with the linear momentum and spin pointing in the same direction.