Irreducible representations of the Heisenberg algebra in Krein spaces

@article{Mnatsakanova1998IrreducibleRO,
  title={Irreducible representations of the Heisenberg algebra in Krein spaces},
  author={Melita Mnatsakanova and G. Morchio and Franco Strocchi and Yu. S. Vernov},
  journal={Journal of Mathematical Physics},
  year={1998},
  volume={39},
  pages={2969-2982}
}
The representations of the Heisenberg algebra in Krein spaces, more generally in weakly complete inner product spaces, are classified under general regularity and irreducibility conditions. Besides the Fock representation, two other types appear; one with negative, the other with a two-sided discrete spectrum of the number operator. 
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References

SHOWING 1-10 OF 21 REFERENCES
Theory of group representations and applications
The material collected in this book originated from lectures given by authors over many years in Warsaw, Trieste, Schladming, Istanbul, Goteborg and Boulder. There is no other comparable book on
Self-adjoint algebras of unbounded operators
Unbounded *-representations of *-algebras are studied. Representations called self-adjoint representations are defined in analogy to the definition of a self-adjoint operator. It is shown that for
Proof of the charge superselection rule in local relativistic quantum field theory
The paper interprets and proves the charge superselection rule within the framework of local relativistic field theory as the statement that the charge operator commutes with all quasilocal
Indefinite Inner Product Spaces
I. Inner Product Spaces without Topology.- 1. Vector Spaces.- 2. Inner Products.- 3. Orthogonality.- 4. Isotropic Vectors.- 5. Maximal Non-degenerate Subspaces.- 6. Maximal Semi-definite Subspaces.-
The physical principles of the quantum theory
The object of this paper is to reformulate the principles of the quantum theory as a sequence of propositions which shall be either summary statements of standard experimental procedure or hypotheses
Mathematical Foundations of Quantum Mechanics
Mathematical Foundations of Quantum Mechanics was a revolutionary book that caused a sea change in theoretical physics. Here, John von Neumann, one of the leading mathematicians of the twentieth
Bakerian Lecture - The physical interpretation of quantum mechanics
  • P. Dirac
  • Physics
    Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1942
Modern developments of atomic theory have required alterations in some of the most fundamental physical ideas. This has resulted in its being usually easier to discover the equations that describe
...
...