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Concepts of coarse graining in quantum mechanics

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Abstract

Various procedures of coarse graining in quantum mechanics and their relationships are reviewed. A recently developed notion of relative coarse graining is described which is based on a certain type of classical embedding of quantum states. The ensuing structure of the set of quantum observables is studied. As an application of the new concept an operational classical limit procedure is sketched out.

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References

  • Ali, S. T., and Prugovečki, E. (1977). Systems of imprimitivity and representations of quantum mechanics on fuzzy phase spaces,Journal of Mathematical Physics,18, 219–228.

    Google Scholar 

  • Bugajski, S. (1991). Nonlinear quantum mechanics is a classical theory,International Journal of Theoretical Physics,30, 961–971.

    Google Scholar 

  • Bugajski, S., Busch, P., Cassinelli, G., Lahti, P. J., and Quadt, R. (1993). Sigma-convex structures and classical embeddings of quantum mechanical state spaces,Reviews in Mathematical Physics, to appear.

  • Busch, P., and Ruch, E. (1992). The measure cone: Irreversibility as a geometrical phenomenon,International Journal of Quantum Chemistry,41, 163–185.

    Google Scholar 

  • Busch, P., Grabowski, M., and Lahti, P. J. (1993). Operational quantum physics, in preparation.

  • Ludwig, G. (1983).Foundations of Quantum Mechanics, Vol. I, Springer-Verlag, Berlin.

    Google Scholar 

  • Ludwig, G. (1987).An Axiomatic Basis for Quantum Mechanics, Vol 2:Quantum Mechanics and Macrosystems, Springer-Verlag, Berlin.

    Google Scholar 

  • Misra, B. (1974). On a new definition of quantal states, inPhysical Reality and Mathematical Description, C. P. Enz and J. Mehra, eds., Reidel, Dordrecht.

    Google Scholar 

  • Prugovečki, E. (1986).Stochastic Quantum Mechanics and Quantum Spacetime, 2nd ed., Reidel, Dordrecht.

    Google Scholar 

  • Quadt, R., and Busch, P. (1993). Coarse graining and the quantum-classical connection,Open Systems and Information Dynamics,2, in press.

  • Ruch, E. (1993). Der Richtungsabstand,Acta Applicandae Mathematicae,30, 67–93.

    Google Scholar 

  • Ruch, E., and Stulpe, W. (1993). On stochastic maps in spaces of bounded additive set functions, in preparation.

  • Schroeck, F. E. (1982). The transitions among classical mechanics, quantum mechanics, and stochastic quantum mechanics,Foundations of Physics,12, 825–841.

    Google Scholar 

  • Singer, M., and Stulpe, W. (1992). Phase-space representations of general statistical physical theories,Journal of Mathematical Physics,33, 131–142.

    Google Scholar 

  • Stulpe, W. (1988). Conditional expectations, conditional distributions, and a posteriori ensembles in generalized probability theory,International Journal of Theoretical Physics,27, 587–611.

    Google Scholar 

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Busch, P., Quadt, R. Concepts of coarse graining in quantum mechanics. Int J Theor Phys 32, 2261–2269 (1993). https://doi.org/10.1007/BF00672998

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