Aspects of conformal strings

Abstract: String theory is the quantum theory in which the fundamental constituents are one-dimensional extended objects in contrast to the usual quantum theories in which the fundamental constituents are point particles. At present we know of only one way to spread out the gravitational interaction and cut off its divergencies without spoiling the consistency of the theory; string theory. This feature together with the possibility of unifying the description of all particles, makes string theory a very promising candidate for a quantum "theory of everything".For very high energies, comparable to or larger than the Planck mass, string theory is truly different from point particle physics and cannot be relpaced by any effective local field theory. Studying the high energy limit may thus lead to some insights into the elusive physical basis of string theory. In string theory the Planck mass is proportional to the square root of the string tension T, so instead of studying the high energy limit one may equivalently study the tensionless limit. It has been found that the tensionless string classically has a larger set of space-time symmetries than the Poincaré group (the symmetry group of the string), viz. the group of space-time conformal transformations.In this thesis we will study a theory which is classically equivalent to the tensionless string, but in which the conformal symmetry is linearly realized and manifest in the formalism, making computations much simpler to perform. Furthermore we use covariant BRST methods which facilitate the computations even more. In particular using BRST methods we investigate the quantum properties of the conformal string, the conformal spinning string and the conformal p-brane which is a generalization of the conformal string to higher dimensional objects.