Note on the point-splitting procedure to evaluate vacuum fluctuation in certain cylindrically symmetric backgrounds
We reexamine the two-point function approaches used to study vacuum fluctuation in wedge-shaped regions and conical backgrounds. The appearance of divergent integrals is discussed and circumvented. The issue is considered in the context of a massless scalar field in cosmic string spacetime.
Abstract In this work, we study the analyticity of Kuramoto–Sivashinsky type equations and related systems by exploring the applicability of the semigroup method, which was developed in Collet et al. [5] . We establish the analyticity, with respect to the spatial variable in a strip around the real axis, for a variety of dissipative–dispersive systems, which possess universal attractors. We also provide lower bounds for the width of the strip of analyticity.