The Classification of Decoherence Functionals: An Analogue of Gleason's Theorem

Details The Classification of Decoherence Functionals: An Analogue of Gleason's Theorem The Classification of Decoherence Functionals: An Analogue of Gleason's Theorem

1994-06-08

arxiv.org/abs/gr-qc/9406015v1

J.Math.Phys. 35 (1994) 6360-6370

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 Pages, Imperial/TP/93--94/42, DAMTP 94--44

Scientific paper

10.1063/1.530679

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 lattice of projectors $\PV$ in some Hilbert space $\V$; in effect we seek the history analogue of Gleason's famous theorem in standard quantum theory. In the present paper we present the solution to this problem for the case where $\V$ is finite-dimensional. In particular, we show that every decoherence functional $d(\a,\b)$, $\a,\b\in\PV$ can be written in the form $d(\a,\b)=\tr_{\V\otimes\V}(\a\otimes\b X)$ for some operator $X$ on the tensor product space $\V\otimes\V$.

Affiliated with

Also associated with

No associations

Rating

The Classification of Decoherence Functionals: An Analogue of Gleason's Theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Classification of Decoherence Functionals: An Analogue of Gleason's Theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Classification of Decoherence Functionals: An Analogue of Gleason's Theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-218366