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Lüders Rule

  • Paul Busch
  • Pekka Lahti

Lüders measurements offer an important characterization of the compatibility of ►observables A,B with discrete spectra: A and B commute if and only if the expectation value of B is not changed by a nonselective Lüders operation of A in any state T [1]. This result is the basis for the axiom of local commutativity in relativistic quantum field theory: the mutual commutativity of observables from local algebras associated with two spacelike separated regions of spacetime ensures, and is necessitated by, the impossibility of influencing the outcomes of measurements in one region through nonselective measurements performed in the other region.

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Primary Literature

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    G. Lüders: Über die Zustandsänderung durch den Meßprozeß, Annalen der Physik 8, 322–328 (1951), available on-line at http://www.physik.uni-augsburg.de/annalen/history/historic-papers/1951_443_322-328.pdf English translation by K.A. Kirkpatrick: Concerning the state-change due to the measurement process, Ann. Phys. (Leipzig) 15, 663–670 (2006)zbMATHGoogle Scholar
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Secondary Literature

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    P. Busch, P. Lahti, P. Mittelstaedt: The Quantum Theory of Measurement (Springer, Berlin 1991, 2nd revised edn. 1996)Google Scholar
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    P. Busch, J. Singh: Lüders theorem for unsharp quantum measurements, Physics Letters A 249, 10–12 (1998)CrossRefADSGoogle Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Paul Busch
  • Pekka Lahti

There are no affiliations available

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