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

Click For Summary

Discussion Overview

The discussion revolves around the role and behavior of spinors in 1+1 dimensional spacetime, particularly in relation to the Dirac equation. Participants explore the concept of "funky" weird stuff associated with spinors, questioning their properties and implications in this lower-dimensional context.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants assert that spinors are necessary for the Dirac equation in 1+1 dimensions, questioning what "funky" weird stuff they might exhibit.
  • There is uncertainty about the definition of "funky" weird stuff, with different authors potentially using varying interpretations.
  • One participant expresses skepticism about the existence of angular momentum in one spatial dimension, raising questions about the nature of spin in this context.
  • Another participant notes that the two components of the Dirac spinor in 1+1 dimensions may represent intrinsic spin and the distinction between particles and antiparticles or positive and negative energy solutions.
  • A later reply suggests that the properties of spinors might only exhibit "funky" behavior in higher dimensions, specifically 3+1 spacetime.
  • One participant references a Wikipedia page to highlight the potential for various spinning phenomena in 1+1 dimensions, questioning what that might entail.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the nature of spinors in 1+1 dimensions, with multiple competing views and definitions of "funky" weird stuff remaining unresolved.

Contextual Notes

There are limitations in the discussion regarding the assumptions about spin and angular momentum in lower dimensions, as well as the definitions of terms used by participants.

Spinnor
Gold Member
Messages
2,231
Reaction score
419
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!
 
Physics news on Phys.org
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?
 
What is "funky" weird stuff? Spin is quantized angular momentum. I'm not sure how you can have angular momentum in one spatial dimension.
 
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
 
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.
 
What if any physics is encoded in the 2 component spinor?
 
Last edited:

Similar threads

Graduate Spinors in dimensions other than 4
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Dirac spinor in 1+1d, do the 2 components represent spin?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Understanding Dirac Equation Spinor Boosts
  • · Replies 7 ·
Replies
7
Views
3K
Graduate Are there two different adjoint representations used in the SM?
  • · Replies 9 ·
Replies
9
Views
2K
Graduate In what representation do Dirac adjoint spinors lie?
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Graph sol. of Dirac eq., type "graph paper" needed?
  • · Replies 4 ·
Replies
4
Views
1K
Graduate How Should I Think About the Dirac Equation
  • · Replies 13 ·
Replies
13
Views
3K
Undergrad The 4 solutions to the Dirac equation
  • · Replies 6 ·
Replies
6
Views
4K
Undergrad The standard model from loop quantum gravity via spinors octonions
  • · Replies 26 ·
Replies
26
Views
6K
Graduate Representation of Lorentz group and spinors (in Peskin page 38)
  • · Replies 13 ·
Replies
13
Views
3K