Note on the point-splitting procedure to evaluate vacuum fluctuation in   certain cylindrically symmetric backgrounds
  We revisit two-point function approaches used to study vacuum fluctuation in wedge-shaped regions and conical backgrounds. Appearance of divergent integrals is discussed and circumvented. The issue is considered in the context of a massless scalar field in cosmic string spacetime. 
I. Brevik, G.E.A. Matsas and E.S. Moreira Jr