On joint distribution in quantum logics. I. Compatible observables

Anatolij Dvurečenskij

Aplikace matematiky (1987)

  • Volume: 32, Issue: 6, page 427-435
  • ISSN: 0862-7940

Abstract

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The notion of a joint distribution in σ -finite measures of observables of a quantum logic defined on some system of σ -independent Boolean sub- σ -algebras of a Boolean σ -algebra is studied. In the present first part of the paper the author studies a joint distribution of compatible observables. It is shown that it may exists, although a joint obsevable of compatible observables need not exist.

How to cite

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Dvurečenskij, Anatolij. "On joint distribution in quantum logics. I. Compatible observables." Aplikace matematiky 32.6 (1987): 427-435. <http://eudml.org/doc/15513>.

@article{Dvurečenskij1987,
abstract = {The notion of a joint distribution in $\sigma $-finite measures of observables of a quantum logic defined on some system of $\sigma $-independent Boolean sub-$\sigma $-algebras of a Boolean $\sigma $-algebra is studied. In the present first part of the paper the author studies a joint distribution of compatible observables. It is shown that it may exists, although a joint obsevable of compatible observables need not exist.},
author = {Dvurečenskij, Anatolij},
journal = {Aplikace matematiky},
keywords = {compatibility; orthomodular poset; observables; joint distribution; measure; quantum logic; compatibility; orthomodular poset; observables; joint distribution; measure},
language = {eng},
number = {6},
pages = {427-435},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On joint distribution in quantum logics. I. Compatible observables},
url = {http://eudml.org/doc/15513},
volume = {32},
year = {1987},
}

TY - JOUR
AU - Dvurečenskij, Anatolij
TI - On joint distribution in quantum logics. I. Compatible observables
JO - Aplikace matematiky
PY - 1987
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 32
IS - 6
SP - 427
EP - 435
AB - The notion of a joint distribution in $\sigma $-finite measures of observables of a quantum logic defined on some system of $\sigma $-independent Boolean sub-$\sigma $-algebras of a Boolean $\sigma $-algebra is studied. In the present first part of the paper the author studies a joint distribution of compatible observables. It is shown that it may exists, although a joint obsevable of compatible observables need not exist.
LA - eng
KW - compatibility; orthomodular poset; observables; joint distribution; measure; quantum logic; compatibility; orthomodular poset; observables; joint distribution; measure
UR - http://eudml.org/doc/15513
ER -

References

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  1. F. S. Varadarajan, Geometry of Quantum Theory, Van Nostrand, Princeton (1968). (1968) Zbl0155.56802
  2. R. Sikorski, Boolean Algebras, Springer-Verlag (1964). (1964) Zbl0123.01303MR0126393
  3. G. Kalmbach, Orthomodular Lattices, Acad. Press, London (1983). (1983) Zbl0528.06012MR0716496
  4. S. P. Gudder, Some unsolved problems in quantum logics, in: Mathematical foundations of quantum theory, A. R. Marlow ed. p. 87-103, Acad. Press, New York (1978). (1978) MR0495813
  5. S. P. Gudder, Joint distributions of observables, J. Math. Mech. 18, 325-335 (1968). (1968) Zbl0241.60092MR0232582
  6. A. Dvurečenskij S. Pulmannová, On joint distributions of observables, Math. Slovaca 32, 155-166 (1982). (1982) MR0658249
  7. A. Dvurečenskij S. Pulmannová, 10.1016/0034-4877(84)90007-7, Rep. Math. Phys. 19, 349-359 (1984). (1984) MR0745430DOI10.1016/0034-4877(84)90007-7
  8. A. Dvurečenskij, On two problems of quantum logics, Math. Slovaca 36, 253-265 (1986). (1986) MR0866626
  9. S. Pulmannová, Compatibility and partial compatibility in quantum logics, Ann. Inst. Henri Poincaré, 34, 391-403. (1981). (1981) MR0625170
  10. S. Pulmannová A. Dvurečenskij, Uncertainty principle and joint distribution of observables, Ann. Inst. Henri Poincaré 42, 253-265 (1985). (1985) MR0797275
  11. S. Pulmannová, Commutators in orthomodular lattices, Demonstratio Math., 18, 187-208 (1985). (1985) MR0816029
  12. A. Dvurečenskij, Joint distributions of observables and measures with infinite values, JINR, E 5-85-867, Dubna (1985). (1985) 
  13. P. Pták, Spaces of observables, Czech. Math. J. 34 (109), 552-561 (1984). (1984) MR0764437
  14. L. H. Loomis, 10.1090/S0002-9904-1947-08866-2, Bull. Amer. Math. Soc. 53, 757-760 (1947). (1947) Zbl0033.01103MR0021084DOI10.1090/S0002-9904-1947-08866-2
  15. M. Duchoň, A note on measures in Cartesian products, Acta F. R. N. Univ. Comen. Math., 23, 39-45 (1969). (1969) MR0265546
  16. G. Birkhoff, Lattice Theory, Nauka, Moscow (1984). (1984) MR0751233
  17. P. R. Halmos, Measure Theory, IIL Moscow (1953). (1953) 
  18. R. Sikorski, On an analogy between measures and homomorphisms, Ann. Soc. Pol. Math., 23, 1-20 (1950). (1950) Zbl0041.17804MR0039697

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