Correlation functions of twist fields from Ward identities in the massive Dirac theory

摘要: We derive non-linear differential equations for correlation functions of U(1) twist fields in the two-dimensional massive Dirac theory. Primary correspond to exponential sine-Gordon model at free-fermion point, and it is well-known that their vacuum two-point are determined by integrable equations. extend part this result more general quantum states (pure or mixed) certain descendents, showing some sinh-Gordon whenever there translation parity invariance, density matrix a bilinear expression fermions. use methods involving Ward identities associated copy-rotation symmetry with two independent, anti-commuting copies. Such were used context thermally perturbed Ising field theory model. show they applicable as well, we suggest likely have much wider applicability free fermion models general. Finally, note our form-factor study descendents combined CFT analysis provides new way evaluating expectation values primary fields: deriving solving recursion relation.