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

In summary, the Dirac equation in 3+1 space-time yields spin, but in 1+1d space-time, where there are no rotations, the concept of angular momentum doesn't make much sense. It is unclear what the 2 components of the spinor represent in this context. One potential area to explore is the current 2 vector, J_μ, which involves the spinors.
  • #1
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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  • #2
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 :-).
 
  • #3
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?
 

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

1. What is a Dirac spinor in 1+1d?

A Dirac spinor in 1+1d is a mathematical object that describes the spin of a particle in a two-dimensional space-time. It is a solution to the Dirac equation, which is a relativistic wave equation that describes the behavior of fermions.

2. How is a Dirac spinor represented in 1+1d?

In 1+1d, a Dirac spinor is represented by a two-component column vector, with each component representing the spin state of the particle. The first component represents the spin-up state, while the second component represents the spin-down state.

3. Do the 2 components of a Dirac spinor represent spin?

Yes, the two components of a Dirac spinor do represent spin. The first component corresponds to the spin-up state, while the second component corresponds to the spin-down state. The spin of a particle can be measured by applying a magnetic field and observing the direction of the particle's spin.

4. How does a Dirac spinor behave under Lorentz transformations?

A Dirac spinor transforms under Lorentz transformations just like any other spinor, following the rules of special relativity. This means that the components of the spinor will change as the particle moves at high speeds, but the overall structure of the spinor remains the same.

5. What is the significance of the Dirac spinor in 1+1d?

The Dirac spinor in 1+1d is significant because it describes the spin of fermions in a two-dimensional space-time, which is relevant in many areas of physics, including quantum field theory and condensed matter physics. It also allows for the prediction and understanding of various physical phenomena, such as the spin of particles in a magnetic field.

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