Foundations of Quantum Theory

Introduction.- Part I Co(X) and B(H): Classical physics on a finite phase space.- Quantum mechanics on a finite-dimensional Hilbert space.- Classical physics on a general phase space.- Quantum physics on a general Hilbert space.- Symmetry in quantum mechanics.- Part II Between Co(X) and B(H): Classical models of quantum mechanics.- Limits: Small hbar.- Limits: large N.- Symmetry in algebraic quantum theory.- Spontaneous Symmetry Breaking.- The Measurement Problem.- Topos theory and quantum logic.- Appendix A: Finite-dimensional Hilbert spaces.- Appendix B: Basic functional analysis.- Appendix C: Operator algebras.- Appendix D: Lattices and logic.- Appendix E: Category theory and topos theory.- References.