Reduction of Lie-Jordan Banach algebras and quantum states Articles uri icon

publication date

  • January 2013

start page

  • 1

end page

  • 14


  • 1 (015201)


  • 46

International Standard Serial Number (ISSN)

  • 1751-8113

Electronic International Standard Serial Number (EISSN)

  • 1751-8121


  • In this paper, it is shown that the concept of dynamical correspondence for Jordan Banach algebras is equivalent to a Lie structure compatible with the Jordan one. Then a theory of reduction of Lie-Jordan Banach algebras in the presence of quantum constraints is presented and compared to the standard reduction of C-*-algebras of observables of a quantum system. The space of states of the reduced Lie-Jordan Banach algebra is characterized in terms of Dirac states on the physical algebra of observables and its GNS representations described in terms of states on the unreduced algebra.


  • mathematical physics; quantum information and quantum mechanics