Bosonization in the path integral formulation

Kazuo Fujikawa; Hiroshi Suzuki

doi:10.1103/PhysRevD.91.065010

paper

Bosonization in the path integral formulation

arXiv:1501.00766 · doi:10.1103/PhysRevD.91.065010

Abstract

We establish the direct $d = 2$ on-shell bosonization $ψ_{L} (x_{+}) = e^{i ξ (x_{+})}$ and $ψ_{R}^{†} (x_{-}) = e^{i ξ (x_{-})}$ in path integral formulation by deriving the off-shell relations $ψ_{L} (x) ψ_{R}^{†} (x) = exp [i ξ (x)]$ and $ψ_{R} (x) ψ_{L}^{†} (x) = exp [- i ξ (x)]$ . Similarly, the on-shell bosonization of the bosonic commuting spinor, $ϕ_{L} (x_{+}) = i e^{- i ξ (x_{+})} \partial^{+} e^{- i χ (x_{+})}$ , $ϕ_{R}^{†} (x_{-}) = e^{- i ξ (x_{-}) - i χ (x_{-})}$ and $ϕ_{R} (x_{-}) = i e^{i ξ (x_{-})} \partial^{-} e^{+ i χ (x_{-})}$ , $ϕ_{L}^{†} (x_{+}) = e^{i ξ (x_{+}) + i χ (x_{+})}$ , is established in path integral formulation by deriving the off-shell relations $ϕ_{L} (x) ϕ_{R}^{†} (x) = i e^{- i ξ (x)} \partial^{+} e^{- i χ (x)}$ and $ϕ_{R} (x) ϕ_{L}^{†} (x) = i e^{i ξ (x)} \partial^{-} e^{i χ (x)}$ .

arXiv comment18 pages, the final version to appear in Phys. Rev. D

Bosonization in the path integral formulation

Abstract

References in corpus (16)