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Communications in Mathematical Physics

, Volume 37, Issue 3, pp 221–256 | Cite as

Generalized quantum mechanics

  • Bogdan Mielnik
Article

Abstract

A convex scheme of quantum theory is outlined where the states are not necessarily the density matrices in a Hilbert space. The physical interpretation of the scheme is given in terms of generalized “impossibility principles”. The geometry of the convex set of all pure and mixed states (called a statistical figure) is conditioned by the dynamics of the system. This provides a method of constructing the statistical figures for non-linear variants of quantum mechanics where the superposition principle is no longer valid. Examples of that construction are given and its possible significance for the interrelation between quantum theory and general relativity is discussed.

Keywords

Neural Network Statistical Physic Hilbert Space General Relativity Complex System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • Bogdan Mielnik
    • 1
  1. 1.Institute of Theoretical PhysicsDivision of Mathematical PhysicsWarszawaPoland

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