Axiom System and Completeness Expression for Quantum Mechanics

The standard axiomatization of quantum mechanics (QM) is not fully explicit about the role of the time-parameter. Especially, the time reference within the probability algorithm (the Born Rule, BR) is unclear. Using a plausible principle P1, about the role of probability in a physical theory, and a second principle P2 affording a most natural way to make BR precise, a logical conflict with the standard expression for the completeness of QM can be derived. Rejecting P1 is implausible. Rejecting P2 leads to unphysical results and to a conflict with a generalization of P2, a principle P3. It is thus made plausible that the standard expression of QM completeness must be revised. An absolutely explicit form of the axioms is provided, including a precise form of the projection postulate. An appropriate expression for QM completeness, reflecting the restrictions of the Gleason and Kochen-Specker theorems is proposed.Comment: 20 pages, no figure

Charge instabilities at the metamagnetic transition

We investigate instabilities in the charge channel in the vicinity of (meta-)magnetic transitions of itinerant electron systems. Based on a weak coupling analysis we argue that in a one-band $t$-$t'$ Hubbard model near the van Hove filling and dominant ferromagnetic fluctuations it is difficult to account for a microscopic mechanism for a d-wave Pomeranchuk deformation of the Fermi surface. A similar deformation has been considered for the metamagnetic transition in Sr$_3$Ru$_2$O$_7$. As an alternative we discuss the possibility of charge inhomogeneity on the nano scale. This extends the analogy of the metamagnetic transition to a liquid-gas transition.Comment: 4 pages, 2 figure