Do spinors still do "funky" weird stuff in 1+1 spacetime?

In summary: What if any physics is encoded in the 2 component spinor?There is no clear consensus on what "funky" weird stuff means in this context. However, it is possible that spinors might still have some interesting transformation properties in 1+1d spacetime.
  • #1
Spinnor
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Apparently we still need spinors for the Dirac equation in 1+1 dimensional space-time. Do spinors still do "funky" weird stuff in 1+1 dimensional space-time?

Thanks for any help!
 
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  • #2
Spinnor said:
Apparently we still need spinors for the Dirac equation in 1+1 dimensional space-time. Do spinors still do "funky" weird stuff in 1+1 dimensional space-time?

Thanks for any help!

Different authors use slightly different definitions for "funky weird stuff". Which definition are you using?
 
  • #3
What is "funky" weird stuff? Spin is quantized angular momentum. I'm not sure how you can have angular momentum in one spatial dimension.
 
  • #4
Khashishi said:
What is "funky" weird stuff? Spin is quantized angular momentum. I'm not sure how you can have angular momentum in one spatial dimension.

Why does the Dirac equation in 1+1 dimensions use 2 component spinors but more important what do the 2 compontents ? See the link below for a good paper on the Dirac equation in 1+1 d.

http://academic.reed.edu/physics/faculty/wheeler/documents/Classical Field Theory/Miscellaneous Essays/A. 2D Dirac Equation.pdf
stevendaryl said:
Different authors use slightly different definitions for "funky weird stuff". Which definition are you using?

Maybe spinors only do "funky" weird stuff in 3+1 spacetime? Funky, like a 4pi rotation is the same as no rotation. Why do we need spinors in 1+1d spacetime and do they have any interesting transformation properties?

See link below for a nice paper on the Dirac equation in 1+1d spacetime.

http://academic.reed.edu/physics/faculty/wheeler/documents/Classical Field Theory/Miscellaneous Essays/A. 2D Dirac Equation.pdf
 
  • #5
The components of the Dirac spinor capture two different things: instrinsic spin, and particles/antiparticles (or positive/negative energy solutions). It works out perfectly in 3+1 spacetime dimensions, because there are 4 components to the spinor, and 4 combinations of types of particle: spin-up and positive energy, spin-up and negative energy, spin-down and positive energy, spin-down and negative energy.

In 1+1 spacetime dimensions, you still have positive/negative energy solutions.
 
  • #6
What if any physics is encoded in the 2 component spinor?
 
  • #7
Last edited:

1. What are spinors?

Spinors are mathematical objects used in quantum mechanics to describe the intrinsic angular momentum (spin) of particles. They are represented by complex numbers and have special properties under rotations in space.

2. What is 1+1 spacetime?

1+1 spacetime refers to a 1-dimensional space and 1-dimensional time. This means that there is only one spatial dimension and one temporal dimension in this space-time.

3. Do spinors behave differently in 1+1 spacetime compared to higher dimensions?

Yes, spinors behave differently in 1+1 spacetime compared to higher dimensions. In higher dimensions, spinors are represented by complex matrices, but in 1+1 spacetime they are represented by complex numbers. This leads to different behaviors and properties.

4. Why do spinors behave differently in 1+1 spacetime?

This is due to the fact that in higher dimensions, rotations involve more complex transformations, while in 1+1 spacetime, rotations are simpler and can be described using only one parameter. This difference in the mathematical structure leads to different behaviors of spinors.

5. Can spinors still exhibit "funky" weird behavior in 1+1 spacetime?

Yes, even though spinors behave differently in 1+1 spacetime, they can still exhibit "funky" weird behavior. For example, they can still undergo reflections and rotations that are not possible for other objects in this spacetime. However, these behaviors may be more limited compared to higher dimensions due to the simpler structure of 1+1 spacetime.

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