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Spinnor
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Can a point in S^3 be uniquely labeled by a 2 component Spinor?
Thanks for any help!
Thanks for any help!
Spinnor said:...
If so I wonder if a spinor times exp(iωt) could be thought of as an orbit in S^3?...
Spinnor said:...
A general path looks like?
Thanks for any help!
Spinnor said:Let ω = 1 and let t = 0, at what time t do we come back to our starting place,
a) t = ∏/2
b) t = ∏
c) t = 2∏
d) t = 4∏
Thanks for any help!
fzero said:Yes, because [itex]SU(2)[/itex] is isomorphic to [itex]S^3[/itex]. We can represent a arbitrary [itex]SU(2)[/itex] matrix by
[tex] U = \begin{pmatrix} z_1 & -z^*_2 \\ z_2 & z_1^*\end{pmatrix}, ~~ |z_1|^2 +|z_2|^2=1.[/tex]
...
A 2 component Spinor is a mathematical object used in theoretical physics to describe the spin of a particle. It is a complex vector with two components that transforms under rotations and has both a magnitude and direction.
Labeling a point in S^3 with a 2 component Spinor allows us to describe the rotation and orientation of a particle in three-dimensional space. It is a useful tool in understanding the behavior of particles and their interactions.
A 2 component Spinor uniquely labels a point in S^3 by representing the rotation and orientation of a particle in three-dimensional space. This is achieved through a mathematical mapping between the 2 component Spinor and the point in S^3.
Yes, there is a difference. A 2 component Spinor contains complex numbers and has a different mathematical structure compared to a 3 component vector. Additionally, the 2 component Spinor allows for a more efficient and elegant description of rotations and orientations in three-dimensional space.
Yes, any point in S^3 can be uniquely labeled with a 2 component Spinor. This is because S^3 is a three-dimensional space and a 2 component Spinor is specifically designed to describe rotations and orientations in three dimensions.