Weak and strong quantum vacuum: Properties of the different vacua

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Abstract
The ideas, definitions, and results of Castagnino and of Castagnino and Mazzitelli are improved and developed in a more general geometry. Also, a more satisfactory definition of the weak vacuum (defined by the coincidence of a local and a global property up to the lowest order) is introduced which yields a renormalization vacuum expectation value of the energy-momentum tensor. It is proved that a strong vacuum (defined by the same coincidence up to all orders) exists only in two particular cases: if there exists a Killing vector field or in the conformal massless case.