In this thesis we study conformal invariance of two-dimensional physical systems, and its connections to the Virasoro algebra. We first discuss how symmetries relate to Lie algebras, and how the...Show moreIn this thesis we study conformal invariance of two-dimensional physical systems, and its connections to the Virasoro algebra. We first discuss how symmetries relate to Lie algebras, and how the Virasoro algebra corresponds to conformal symmetries. We then study the theory of the free open bosonic string. Starting with the Nambu-Goto action, we first solve the equations of motion of the classical string using the light-cone gauge. From there, we construct the quantum theory and show it is indeed a representation of the Virasoro algebra. We then look more directly into representations of the Virasoro algebra. We define lowest weight representations and Verma modules, and discuss reducibility of the latter.Show less
