Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Erratum: Simple Groups and Strong Interaction Symmetries

Erratum: Simple Groups and Strong Interaction Symmetries other two Murray-von Neumann types of infinite unitary representations in that it alone would retain (like the finite-dimensional case which it includes) a certain uniqueness of decomposition into reps- uniqueness but not necessarily discreteness since it may involve either a continuous-discrete sum or a discrete-continuous sum. "For physics we may add the following comments: The concept of multiplicity-freeness enables us to de- fine quite generally the conditions on a set of obseryv- ables such that, when the observables are measured, the quantum mechanical state is completely specified. In other words the concept of 'multiplicity freeness' permits us to state more concisely a general defini- tion which Jauch (1960, 1961) has given of 'a com- plete set of commuting observables.' This definition applies equally well to operators with continuous as with discrete spectra-in contrast with the usual definition of a complete commuting set, requiring that there occur only nondegenerate common eigen- values. Suppose L is the set of all bounded functions generated by a set of commuting observables. Then L is the smallest 'weakly closed' algebra2 containing the original set. By a theorem of von Neumann (1929) any such 'smallest weakly closed algebra' is equal to its double commutant, http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reviews of Modern Physics American Physical Society (APS)

Erratum: Simple Groups and Strong Interaction Symmetries

Loading next page...
 
/lp/american-physical-society-aps/erratum-simple-groups-and-strong-interaction-symmetries-6lX0g6zlEE

References

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher
American Physical Society (APS)
Copyright
Copyright © 1962 The American Physical Society
ISSN
1539-0756
DOI
10.1103/RevModPhys.34.584
Publisher site
See Article on Publisher Site

Abstract

other two Murray-von Neumann types of infinite unitary representations in that it alone would retain (like the finite-dimensional case which it includes) a certain uniqueness of decomposition into reps- uniqueness but not necessarily discreteness since it may involve either a continuous-discrete sum or a discrete-continuous sum. "For physics we may add the following comments: The concept of multiplicity-freeness enables us to de- fine quite generally the conditions on a set of obseryv- ables such that, when the observables are measured, the quantum mechanical state is completely specified. In other words the concept of 'multiplicity freeness' permits us to state more concisely a general defini- tion which Jauch (1960, 1961) has given of 'a com- plete set of commuting observables.' This definition applies equally well to operators with continuous as with discrete spectra-in contrast with the usual definition of a complete commuting set, requiring that there occur only nondegenerate common eigen- values. Suppose L is the set of all bounded functions generated by a set of commuting observables. Then L is the smallest 'weakly closed' algebra2 containing the original set. By a theorem of von Neumann (1929) any such 'smallest weakly closed algebra' is equal to its double commutant,

Journal

Reviews of Modern PhysicsAmerican Physical Society (APS)

Published: Jul 1, 1962

There are no references for this article.