Non-local representation of (2+1)-dimensional quantum gravity with spinor field

Abstract

Non-local representation of(2+1)-dimensional quantum gravity coupled with the spinor field is considered. We first introduce non-local variables and obtain non-local quantities that are equivalent to the local constraints in some limit. The quantization of these non-local variables is executed in a non-local representation that is similar to the loop representation of pure gravity. The contribution of spinor fields in the state functionals depends not only on the space of loops but also on the space of lines. A state functional which is the solution of all constraint equations is also obtained.