The cosmological constant and volume-preserving diffeomorphism invariants

Abstract

Observables in the quantum field theories of ( D − 1)-form fields, A , on D-dimensional, compact and orientable manifolds, M, are computed. Computations of the vacuum value of the energy-momentum tensor, 〈 T ab 〉, on manifolds without boundaries, find it to be the metric times a function of the volume of spacetime, Ω(M). Whereas, on manifolds with boundaries, 〈 T ab 〉 is of the form due to a cosmological constant. The correlation functions of another set of operators give intersection numbers on M. Furthermore, a similar computation for products of Wilson area operators results in a function of the volumes of the intersections of the submanifolds the operators are defined on. In addition, scalar field couplings are introduced and potentials are induced after integrating out the A -field. Lastly, the thermodynamics of the pure theories is found to be analogous to the zero-point motion of a scalar particle.