What's the meaning of spin in 1+1 spacetime?

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SUMMARY

The discussion centers on the interpretation of spin in 1+1 dimensional spacetime, particularly in the context of the Schwinger model. Participants clarify that while the electron field is often referred to as spin-1/2 and the electromagnetic field as spin-1, these designations arise from the properties of the SO(1,1) Lorentz group rather than traditional rotational symmetry. The conversation emphasizes that two-component spinors and gamma matrix representations can be constructed using Pauli matrices, drawing parallels to higher-dimensional spin concepts despite the absence of conventional rotations.

PREREQUISITES
  • Understanding of the Schwinger model
  • Familiarity with SO(1,1) Lorentz group
  • Knowledge of two-component spinors
  • Basic grasp of gamma matrices and Pauli matrices
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  • Research the mathematical framework of the Schwinger model
  • Explore the properties of the SO(1,1) Lorentz group
  • Study the construction of two-component spinors in quantum field theory
  • Learn about the role of gamma matrices in different dimensional spacetimes
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The discussion is beneficial for theoretical physicists, quantum field theorists, and students of advanced physics interested in the nuances of spin in lower-dimensional spacetimes.

ingenue
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When people discuss the Schwinger model, sometimes they still call the electron field spin-1/2 and the EM field spin-1. I wonder if there's some justification for these calling, since there's no rotations at all in 1+1 spacetime. I know for SO(n) with n>=2, one can always have well-defined spins.
 
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In 1+1 dim. the spin comes from the SO(1,1) Lorentz group. There are two-component spinors, a gamma matrix representation can be constructed from the Pauli matrices.

Of course there is no rotation in the ordinary sense, but the mathematics underlying spin is similar to the 3+1 dim case.
 

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