Lorentzian 2D CFT from the pAQFT Perspective

We provide a detailed construction of the quantum theory massless scalar field on 2-dimensional, globally-hyperbolic (in particular, Lorentzian) manifolds using framework perturbative algebraic theory. From this we subalgebras observables isomorphic to Heisenberg and Virasoro algebras Einstein cylinder. also show how conformal version general covariance, as first introduced by Pinamonti an extension due Brunetti, Fredenhagen Verch, may be applied concept natural Lagrangians in order obtain simple condition for covariance classical dynamics, which is then shown quantise case quadratic Lagrangian. compare stress-energy tensor Minkowksi space, obtaining transformation law dependent Schwarzian derivative transformed coordinate, accordance with well-known result Euclidean literature.