Quantum States and Measures on the Spectral Presheaf
After a brief introduction to the spectral presheaf, which serves as an analogue of state space in the topos approach to quantum theory, we show that every state ρ of the von Neumann algebra N of physical quantities of a quantum system determines a certain measure μρ on the spectral presheaf of the system. The so-called clopen subobjects of the spectral presheaf play the role of measurable sets. Measures on the spectral presheaf can be characterised abstractly, and the main result is that every abstract measure μ induces a unique state ρμ of the von Neumann algebra N. Finally, we show how quantum-theoretical expectation values can be calculated from measures associated to quantum states.
No Reference information available - sign in for access.
No Citation information available - sign in for access.
No Supplementary Data.
No Article Media
Document Type: Research Article
Publication date: June 1, 2009
More about this publication?
- ADVANCED SCIENCE LETTERS is an international peer-reviewed journal with a very wide-ranging coverage, consolidates research activities in all areas of (1) Physical Sciences, (2) Biological Sciences, (3) Mathematical Sciences, (4) Engineering, (5) Computer and Information Sciences, and (6) Geosciences to publish original short communications, full research papers and timely brief (mini) reviews with authors photo and biography encompassing the basic and applied research and current developments in educational aspects of these scientific areas.
- Editorial Board
- Information for Authors
- Subscribe to this Title
- Ingenta Connect is not responsible for the content or availability of external websites