  In this paper we study a new symmetry argument that results in a vacuum state
with strictly vanishing vacuum energy. This argument exploits the well-known
feature that de Sitter and Anti- de Sitter space are related by analytic
continuation. When we drop boundary and hermiticity conditions on quantum
fields, we get as many negative as positive energy states, which are related by
transformations to complex space. The paper does not directly solve the
cosmological constant problem, but explores a new direction that appears
worthwhile.
