Bosonization in the path integral formulation

Kazuo Fujikawa, Hiroshi Suzuki

We establish the direct $d=2$ on-shell bosonization ${\psi }_L(x_{+})=e^{i\xi (x_{+})}$ and ${\psi }_R^{†}(x_{-})=e^{i\xi (x_{-})}$ in path integral formulation by deriving the off-shell r…