SemiInfinite Homology and 2d Quantum Gravity
Abstract
The primary goal of this thesis is to study the constraint problem for twodimensional quantum gravity in two gaugesthe conformal and the lightcone gauge. In each, case, we examine a natural class of representations of the gravitational sector. We then ask for the physical spectrum when gravity is coupled to conformal matter via the BRST procedure. We classify the free field representations which result in nontrivial physical states, and compute the quantum numbers of these states. Our work also uncovers some infinitely many new physical states beyond those proposed by Knizhnik, Polyakov and Zamolodchikov. These new states are shown to be the continuum counterparts of most of the physical observables in the random matrix models. The principal tool for our investigations is the theory of semiinfinite homology, first introduced and developed by Feigin, and later by Frenkel, Garland and Zuckerman. In solving the constraint problems, we also discuss a number of new results in semiinfinite homology theory.
 Publication:

Ph.D. Thesis
 Pub Date:
 1991
 Bibcode:
 1991PhDT.......242L
 Keywords:

 TWO DIMENSIONAL QUANTUM GRAVITY;
 Physics: Elementary Particles and High Energy; Mathematics