Conformal Symmetry and Chirality in Perturbative Algebraic Quantum Field Theory

The concepts of conformal covariance and chirality in 2 spacetime dimensions are formulated and examined within the perturbative algebraic quantum field theory framework. Firstly the qualitative features of the massless scalar field in 2 dimensions are examined,with a particular focus on the properties which are of general significance in the study of 2-dimensional conformal field theories. A general condition for the extension of covariance under local isometries to conformal covariance is then formulated for classical field theories,which is shown to quantise naturally for non-interacting theories. Features such as primary fields are identified and discussed, leading to a generalisation of the transformation law for the stress-energy tensor of the massless scalar field. Finally, the topic of chirality is discussed. In particular, an emphasis is placed on constructing chiral algebras as natural sub-theories of 2-dimensional conformal field theories on globally hyperbolic Lorentzian manifolds. Cauchy surfaces are used as a natural model for the co-dimension 1 spaces upon which chiral field configurations are defined,until in the final chapter we propose a method by which these algebras may be described without such auxiliary data and in a model-independent way.