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Foundations of quantum theory

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Foundations of quantum theory

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  • Part I C0(X) and B(H)

  • 1 Classical physics on a finite phase space

    • 1.1 Basic constructions of probability theory

    • 1.2 Classical observables and states

    • 1.3 Pure states and transition probabilities

    • 1.4 The logic of classical mechanics

    • 1.5 The GNS-construction for C(X)

    • 2 Quantum mechanics on a finite-dimensional Hilbert space

      • 2.1 Quantum probability theory and the Born rule

      • 2.2 Quantum observables and states

      • 2.3 Pure states in quantum mechanics

      • 2.4 The GNS-construction for matrices

      • 2.5 The Born rule from Bohrification

      • 2.6 The Kadison–Singer Problem

      • 2.8 Proof of Gleason’s Theorem

      • 2.9 Effects and Busch’s Theorem

      • 2.10 The quantum logic of Birkhoff and von Neumann

      • 3 Classical physics on a general phase space

        • 3.1 Vector fields and their flows

        • 3.2 Poisson brackets and Hamiltonian vector fields

        • 3.3 Symmetries of Poisson manifolds

        • 4 Quantum physics on a general Hilbert space

          • 4.1 The Born rule from Bohrification (II)

          • 4.2 Density operators and normal states

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