منابع مشابه
On the Classification of Decoherence Functionals
The basic ingredients of the consistent histories approach to quantum mechanics are the space of histories and the space of decoherence functionals. In this work we extend the classification theorem for decoherence functionals proven by Isham, Linden and Schreckenberg to the case where the space of histories is the lattice of projection operators on an arbitrary separable or non-separable compl...
متن کاملThe Classification of Decoherence Functionals: An Analogue of Gleason’s Theorem
Gell-Mann and Hartle have proposed a significant generalisation of quantum theory with a scheme whose basic ingredients are ‘histories’ and decoherence functionals. Within this scheme it is natural to identify the space UP of propositions about histories with an orthoalgebra or lattice. This raises the important problem of classifying the decoherence functionals in the case where UP is the latt...
متن کاملHilbert Space Representations of Decoherence Functionals and Quantum Measures
We show that any decoherence functional D can be represented by a spanning vector-valued measure on a complex Hilbert space. Moreover, this representation is unique up to an isomorphism when the system is finite. We consider the natural map U from the history Hilbert space K to the standard Hilbert space H of the usual quantum formulation. We show that U is an isomorphism from K onto a closed s...
متن کاملOn Tracial Operator Representations of Quantum Decoherence Functionals
A general quantum history theory can be characterised by the space of histories and by the space of decoherence functionals. In this note we consider the situation where the space of histories is given by the lattice of projection operators on an infinite dimensional Hilbert space H. We study operator representations for decoherence functionals on this space of histories. We first give necessar...
متن کاملThe representation theory of decoherence functionals in history quantum theories
In the first part of this paper the general perspective of history quantum theories is reviewed. History quantum theories provide a conceptual and mathematical framework for formulating quantum theories without a globally defined Hamiltonian time evolution and for introducing the concept of space time event into quantum theory. On a mathematical level a history quantum theory is characterized b...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 1995
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.530916