SU(2) Rotation & Spinors: Connected?

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SUMMARY

In the context of SU(2) rotations, a rotation of 720 degrees is necessary to return to the original state, which aligns with the behavior of spinors. The discussion confirms that rotation in SU(2) implies the rotation of spinors, establishing that spinors are indeed objects affected by SU(2) transformations. This relationship highlights the distinction between spinors and traditional 3-dimensional vectors, which are influenced by SO(3) rotations.

PREREQUISITES
  • Understanding of SU(2) group theory
  • Familiarity with spinors in quantum mechanics
  • Knowledge of SO(3) rotations
  • Basic concepts of angular momentum in physics
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  • Study the mathematical structure of SU(2) and its applications in quantum mechanics
  • Explore the properties and applications of spinors in physics
  • Investigate the relationship between SU(2) and SO(3) transformations
  • Read Bruce Schumm's "Deep Down Things" for deeper insights into these concepts
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Physicists, mathematicians, and students studying quantum mechanics, particularly those interested in the mathematical foundations of spinors and their relation to SU(2) rotations.

HowardTheDuck
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Hi, a fairly quick question. I'm reading Bruce Schumm's book "Deep Down Things" and he says that in SU(2) you have to rotate by 720 degrees to return to your starting point. This is clearly the same definition as a spinor. My question is, then, does rotation in SU(2) automatically imply the rotation of a spinor? Or is a spinor a special case of a rotation in SU(2)? Any help much appreciated.
 
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A spinor is an object on which an element of SU(2) acts, just a physical 3-d vector is an object on which a normal rotation (element of SO(3)) acts.
 
Thanks. So that appears to suggest that, yes, if you are rotating in SU(2) then your objects behave as spinors. Yes, that's surely correct.
 
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