Lorentz Invariant Decompositions of the State Vector Spaces and the Basis Problem

Foundations of Physics 34 (6):987-1003 (2004)

We consider a representation of the state reduction which depends neither on its reality nor on the details of when and how it emerges. Then by means of the representation we find necessary conditions, even if not the sufficient ones, for a decomposition of the state vector space to be a solution to the basis problem. The conditions are that the decomposition should be Lorentz invariant and orthogonal and that the associated projections should be continuous. They are shown to be able to determine a decomposition in each of a few examples considered if the other circumstances are taken into account together
Keywords basis problem  Lorentz invariance  state reduction
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DOI 10.1023/B:FOOP.0000034225.69458.a0
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