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!
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.
stevendaryl said:Different authors use slightly different definitions for "funky weird stuff". Which definition are you using?
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.
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.
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.
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.
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.