"Properly speaking, in 1+1 dim. no such thing as spin, but"

[Spinnor]

Could you please put the conclusion ("The spin-statistics theorem says that in local quantum field theory in two dimensions an anticommuting field must have half-integral Lorentz quantum numbers.") of the following quote in simpler terms if possible,

"Properly speaking, in 1+1 dimensions there is no such thing as spin, but there is a two-dimensional Lorentz group (or local Lorentz group, in the case of a generally covariant theory), and it makes sense to ask how a two-dimensional field transforms under this group. The spin-statistics theorem says that in local quantum field theory in two dimensions an anticommuting field must have half-integral Lorentz quantum numbers."

Quote from Google book search "is there a spin statistics theorem in 1 + 1 spacetime dimensions"

Bottom of page 187, https://books.google.com/books?id=_18hAwAAQBAJ&pg=PA187&dq=string theory: volume 1, introduction&hl=en&sa=X&ei=dr-yVOTQO8rasAStkIGQBg&ved=0CCwQ6AEwAw#v=onepage&q=string theory: volume 1, introduction&f=false

Also does this answer my early question about what the 2 component spinor solutions of the Dirac equation in 1+1 dimensions represent?

Thanks for any help!

 

[eljose79]

In simpler terms, the spin-statistics theorem states that in a two-dimensional world, there is no concept of spin, but there is a two-dimensional Lorentz group that describes how fields behave under transformations. In local quantum field theory, an anticommuting field in two dimensions must have half-integral Lorentz quantum numbers. This means that the field behaves differently under the Lorentz group compared to fields in higher dimensions. And yes, the 2 component spinor solutions of the Dirac equation in 1+1 dimensions represent the behavior of fields under the two-dimensional Lorentz group.