Wedges, Cones, Cosmic Strings, and the Reality of Vacuum Energy

TL;DR

This paper explores how diffraction theory by wedges relates to vacuum energy in cosmic strings and accelerating observers, demonstrating the physical reality of vacuum energy through detailed analysis of scalar fields in related geometries.

Contribution

It clarifies the connection between wedge diffraction problems and vacuum energy in cosmic string and accelerated frames, emphasizing the physical reality of cosmological vacuum energy.

Findings

Vacuum expectation values of energy density and pressure are computed for scalar fields.

Minkowski space vacuum energy arises from quantized angular modes, similar to Casimir energy.

The analysis supports the reality of cosmological vacuum energy.

Abstract

One of J. Stuart Dowker's most significant achievements has been to observe that the theory of diffraction by wedges developed a century ago by Sommerfeld and others provided the key to solving two problems of great interest in general-relativistic quantum field theory during the last quarter of the twentieth century: the vacuum energy associated with an infinitely thin, straight cosmic string, and (after an interchange of time with a space coordinate) the apparent vacuum energy of empty space as viewed by an accelerating observer. In a sense the string problem is more elementary than the wedge, since Sommerfeld's technique was to relate the wedge problem to that of a conical manifold by the method of images. Indeed, Minkowski space, as well as all cone and wedge problems, are related by images to an infinitely sheeted master manifold, which we call Dowker space. We review the research in this area and exhibit in detail the vacuum expectation values of the energy density and pressure of a scalar field in Dowker space and the cone and wedge spaces that result from it. We point out that the (vanishing) vacuum energy of Minkowski space results, from the point of view of Dowker space, from the quantization of angular modes, in precisely the way that the Casimir energy of a toroidal closed universe results from the quantization of Fourier modes; we hope that this understanding dispels any lingering doubts about the reality of cosmological vacuum energy.