Rotational Invariance: Bosons vs Fermions

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Discussion Overview

The discussion revolves around the concept of rotational invariance in relation to bosons and fermions, exploring the implications of 2 pi and 4 pi rotations on particle states and macroscopic objects. It includes theoretical considerations and clarifications regarding the nature of these particles under rotation.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions whether particles invariant under 2 pi rotation are bosons, while those requiring 4 pi rotation are fermions.
  • Another participant clarifies that fermion quantum states are invariant under 2 pi rotations, but the vectors representing these states change phase, specifically by a factor of -1.
  • A participant suggests that macroscopic objects can be viewed as either bosons or a combination of bosons and fermions, proposing that only the bosonic part is observable due to its invariance under 2 pi rotation.
  • Another participant challenges this view, stating that fermion states and observables are also invariant under 2 pi rotations, emphasizing that the observable properties do not differ between fermions and bosons in this context.
  • A later reply reiterates that macroscopic objects are invariant under such rotations, questioning why this would not be the case.

Areas of Agreement / Disagreement

Participants express differing views on the implications of rotational invariance for bosons and fermions, particularly regarding the observability of their properties. There is no consensus on the interpretation of these invariances and their implications for macroscopic objects.

Contextual Notes

The discussion highlights the complexity of phase changes in quantum states and the distinction between observable and non-observable properties, which remains unresolved.

relativityfan
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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
 
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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.
 
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?
 
relativityfan said:
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?

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.
 
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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