# Rotational invariance

1. Oct 12, 2010

### relativityfan

hi,

is it correct to say that any particle or object that is invariant under rotation of 2 pi is a boson, whereas fermions need 4 pi?
what is the accurate statement about this?

thank you for your reply

2. Oct 12, 2010

### arkajad

For fermions quantum states are also invariant with respect to 2pi rotations. But not vectors representing the states. Phase ambiguity in the relation between vectors and states is crucial here. After 2pi rotation vectors change their phase. This change can be reduced to multiplication by -1, but no more.

3. Oct 12, 2010

### relativityfan

macroscopic objects are either bosons or the sum of a boson and a fermion. can we say that we only see the bosonic part since they are invariant with 2pi rotation?

4. Oct 12, 2010

### arkajad

You are making a mistake here. Le me repeat: Fermion states are also invariant under 2pi rotations. The same applies to fermionic observables. For the properties of observables with respect to 2pi rotations there is no difference between Fermions and Bosons.

The difference is at the level that is not observable. It reflects itself in the values of spin, but not in the rotational invariance of states.

5. Oct 12, 2010

### relativityfan

thank you for your reply, but at the level that is not observable, it seems that the conclusion is the same: macroscopic objects taken as a whole are invariant under such rotations because i do not see why the contrary could be true, what do you think?

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