Spin 1/2 vs Spin 2

the electron (a spin 1/2 particle) must turn twice to be back in its original position (so that its complex wave function is identically restore).

Now my question is this:
If a spin 1/2 particle must turn 2*360 for it's wave function to be identical, can we say that a spin 2 particle must turn 360/2 for it's wave function to be identical ?

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samalkhaiat
Now my question is this:
If a spin 1/2 particle must turn 2*360 for it's wave function to be identical, can we say that a spin 2 particle must turn 360/2 for it's wave function to be identical ?
Yes, it is like a two-headed arrow. And spin-1 particle looks the same only if one turns it a 360 degrees, it is like an arrow. Do you know how to represent a spin-0 particle?

sam

Here is a related quote for those interested.
(but it's a bit more than what I can understand myself)
from http://math.ucr.edu/home/baez/week109.html >>

The spin-0 representation is the trivial representation. Physicists call vectors in this representation "scalars", since they are just complex numbers. Particles transforming in the spin-0 representation of SU(2) are also called scalars. Examples include pions and other mesons. The only fundamental scalar particle in the Standard Model is the Higgs boson - hypothesized but still not seen.

The spin-1/2 representation is the fundamental representation, in which SU(2) acts on C^2 in the obvious way. Physicists call vectors in this representation "spinors". Examples of spin-1/2 particles include electrons, protons, neutrons, and neutrinos. The fundamental spin-1/2 particles in the Standard Model are the leptons (electron, muon, tau and their corresponding neutrinos) and quarks.

The spin-1 representation comes from turning elements of SU(2) into 3x3 matrices using the double cover SU(2) → SO(3). This is therefore also called the "vector" representation. The spin-1 particles in the Standard Model are the gauge fields: the photon, the W and Z, and the gluons.

Though you can certainly make composite particles of higher spin, like hadrons and atomic nuclei, there are no fundamental particles of spin greater than 1 in the Standard Model. But the Standard Model doesn't cover gravity. In gravity, the spin-2 representation is very important. This comes from letting SO(3), and thus SU(2), act on symmetric traceless 3x3 matrices in the obvious way (by conjugation). In perturbative quantum gravity, gravitons are expected to be spin-2 particles

No guys i think you are making something wrong....
Representations on wavefunctions by SU(2) is siglevalued on integers spin (s=1,2,3..)
and double valued on half integers (s=1/2,3/2..).
Thats the only motivation...

regards marco.