Excitations and interactions in d = 1 string theory

In this paper, the authors discuss the singlet sector of the d = 1 matrix model in terms of a Dirac fermion formalism. The leading order two- and three-point functions of the density fluctuations are obtained by this method. This allows the authors to construct the effective action to that order and hence provide the equation of motion. This equation is compared with the one obtained from the continuum approach. The authors also compare continuum results for correlation functions with the matrix model ones and discuss the nature of gravitational dressing for this regularization. Finally, the authors address the question of boundary conditions within the framework of the d = 1 unitary matrix model, considered as a regularized version of the Hermitian model, and study the implications of a generalized action with an additional parameter (analogous to the θ parameter) which give rise to quasi-periodic wave functions