Understanding Spinors: Rank-1/2 Tensors & Square Roots of Vectors

[scope]

hi,

can se say loosely that a spinor is a rank-1/2 tensor or the square root of a vector, since a scalar does not change under rotations, a vector changes one time, a rank 2-tensor two times, a rank 3 tensor 3 times, and a spinor 1/2 time.
also a scalar in 4d has 1 component, a vector 4 components, a rank-2 tensor 16 components, and a spin 2 components.

does that make sense?

 

[arkajad]

and a spin 2 components.

Two complex components = four real components.

rank 2-tensor two times...

?

 

[scope]

Two complex components = four real components.



?

yes a rank-2 tensor when we change coordinates, is transformed by multiplying it 2 times by the coordinate transformations, that is the definition of a tensor in physics.

for example if this transformation is a 2pi rotation, the graviton as a tensorial particle is rotated 2 times by 2pi.

 

[arkajad]

Do you want to say that after rotation by pi any rank2 tensor does not change?