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

1. Jan 7, 2015

### Spinnor

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!

2. Jan 8, 2015

### stevendaryl

Staff Emeritus
Different authors use slightly different definitions for "funky weird stuff". Which definition are you using?

3. Jan 8, 2015

### Khashishi

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. Jan 8, 2015

### Spinnor

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
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. Jan 8, 2015

### stevendaryl

Staff Emeritus
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. Jan 8, 2015

### Spinnor

What if any physics is encoded in the 2 component spinor?

7. Jan 8, 2015

### Spinnor

Last edited: Jan 8, 2015