International Journal of Modern Physics A

There has been spectacular progress in the development of string and superstring theories since its inception thirty years ago. Development in this area has never been impeded by the lack of experimental confirmation. Indeed, numerous bold and imaginative strides have been taken and the sheer elegance and logical consistency of the arguments have served as a primary motivation for string theorists to push their formulations ahead. In fact the development in this area has been so rapid that new ideas quickly become obsolete. On the other hand, this rapid development has proved to be the greatest hindrance for novices interested in this area. These notes serve as a gentle introduction to this topic. In these elementary notes, we briefly review the RNS formulation of superstring theory, GSO projection, D-branes, bosonic strings, dualities, dynamics of D-branes and the microscopic description of Bekenstein entropy of a black hole.

We study the SU(n)-invariant massive Thirring model with boundary reflection. Our approach is based on the free field approach. We construct the free field realizations of the boundary state and its dual. For an application of these realizations, we present integral representations for the form factors of the local operators.

Rigid string world sheets in ℝ⁴ are described by means of a representation of the Weierstrass type. Correlators for the full rigid string action in the one-loop approximation over minimal backgrounds are calculated.

In this paper we continue the study of the geometrical features of a functional approach to classical mechanics proposed some time ago. In particular, we try to shed some light on a N = 2 "universal" supersymmetry which seems to have an interesting interplay with the concept of ergodicity of the system. To study the geometry better we make this susy local and clarify pedagogically several issues present in the literature. Secondly, in order to prepare the ground for a better understanding of its relation to ergodicity, we study the system on constant energy surfaces. We find that the procedure of constraining the system on these surfaces injects in it some local Grassmannian invariances and reduces the N = 2 global susy to an N = 1.