Dirac spinor in 1+1d, do the 2 components represent spin?

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SUMMARY

The discussion centers on the representation of spin in 1+1 dimensional space-time using Dirac spinors. Unlike 3+1 dimensions, where the Dirac equation yields intrinsic spin, the concept of spin is less applicable in 1+1 dimensions due to the absence of rotational symmetry. Participants suggest examining the current 2-vector, J_μ, to understand the role of spinors in this context, indicating that the two components of the spinor may not represent traditional spin.

PREREQUISITES
  • Understanding of the Dirac equation in quantum mechanics
  • Familiarity with spinors and their properties
  • Knowledge of angular momentum concepts in physics
  • Basic grasp of 1+1 dimensional space-time implications
NEXT STEPS
  • Research the implications of the Dirac equation in 1+1 dimensions
  • Examine the properties of spinors in low-dimensional space-time
  • Explore the concept of current 2-vectors, specifically J_μ
  • Investigate the relationship between angular momentum and dimensionality in physics
USEFUL FOR

The discussion is beneficial for theoretical physicists, quantum mechanics students, and researchers exploring the implications of spin and dimensionality in quantum field theory.

Spinnor
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The Dirac equation in 3+1 space-time yields spin, is this still true in 1+1d space-time? If not what do the 2 components of the spinor represent? Do we still have intrinsic spin in 1+1d space-time?

Thanks for any help!
 
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In one space dimension, angular momentum doesn't make too much sense, I'd say, because there are no rotations. It's a good question, what it represents! I've no spontaneous idea :-).
 
vanhees71 said:
In one space dimension, angular momentum doesn't make too much sense, I'd say, because there are no rotations. It's a good question, what it represents! I've no spontaneous idea :).

Thank you for help! Would one place to look be to examine the current 2 vector, J_μ? That would involve the spinors?
 

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