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Quantum optical phase, rigged Hilbert spaces and complementarity.

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Summary
This summary is machine-generated.

Loudon's quantum phase theory inspired new formalisms. Pegg and Barnett developed a quantum phase formalism using extended Hilbert spaces, resolving ambiguities in quantum-classical correspondence.

Keywords:
Pegg–Barnett phase formalismcomplementarityquantum phase operatorrigged hilbert spaces

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Area of Science:

  • Quantum optics
  • Quantum mechanics
  • Mathematical physics

Background:

  • Loudon's quantum treatment of optical phase.
  • The quantum theory of light.
  • Historical context of quantum phase.

Purpose of the Study:

  • To place Loudon's quantum phase theory in historical context.
  • To outline research inspired by Loudon's work.
  • To explain the development of the Pegg-Barnett quantum phase formalism.

Main Methods:

  • Historical analysis of quantum phase theory.
  • Examination of the Pegg-Barnett quantum phase formalism.
  • Investigation of extended rigged Hilbert spaces.
  • Identification of complementarity structures.

Main Results:

  • Loudon's work inspired the Pegg-Barnett formalism.
  • The formalism rigorously defines phase operators and eigenstates.
  • An extended rigged Hilbert space supports limits of phase operators.
  • A complementarity structure provides quantum-classical correspondence free of ambiguity.

Conclusions:

  • Pegg and Barnett's formalism offers a rigorous approach to quantum phase.
  • The formalism resolves ambiguities in quantum-classical correspondence.
  • The underlying complementarity structure is key to this advancement.