Group Theoretical Discussion of Relativistic Wave Equations.

@article{Bargmann1948GroupTD,
  title={Group Theoretical Discussion of Relativistic Wave Equations.},
  author={Valentine Bargmann and Eugene Paul Wigner},
  journal={Proceedings of the National Academy of Sciences of the United States of America},
  year={1948},
  volume={34 5},
  pages={
          211-23
        }
}
  • V. BargmannE. Wigner
  • Published 1 May 1948
  • Physics
  • Proceedings of the National Academy of Sciences of the United States of America
1 — The wave functions, ψ, describing the possible states of a quantum mechanical system form a linear vector space V which, in general,. is infinite dimensional and on which a positive definite inner product (φ, ψ) is defined for any two wave functions φ and ψ (i.e., they form a Hilbert space). The inner product usually involves an integration over the whole configuration or momentum space and, for particles of higher spin, a summation over the spin indices. 

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Note on Continuous Representations of Lie Groups.

  • L. Gårding
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1947
Theory of Games and Economic Behavior and Linear Inequalities: A Review of Von Neumann’s Theorem.

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It is perhaps the most fundamental principle of Quantum Mechanics that the system of states forms a linear manifold,1 in which a unitary scalar product is defined.2 The states are generally