Roderich Tumulka:
Topics in Mathematical Physics: Wave Function Collapse, 16:642:662, graduate course, spring 2009
Syllabus:

  1. Overview. The quantum formalism; the quantum measurement problem; the problem about complementarity. Ideas behind hidden variables, spontaneous collapse, many worlds. Example theories: Bohmian mechanics, Ghirardi-Rimini-Weber (GRW), Everett.
  2. The Schrodinger equation; Hilbert space and L2 spaces; configuration space; inner product; orthonormal bases; unitary, self-adjoint, and projection operators; eigenfunctions; the spectral theorem.
  3. Projection-valued measures (PVMs); generalized orthonormal bases; integration over PVMs and operators in general; the spectral theorem in terms of PVMs. Tensor product of Hilbert spaces; entangled wave functions.
  4. Positive-operator-valued measures (POVMs); the generalized quantum formalism (1st half). Primitive ontology (particles, strings, flashes, matter density); GRW theory with flash ontology (= GRWf) given abstractly in terms of POVMs.
  5. Subsystems of a GRW world. Derivation of the generalized quantum formalism (1st half) from abstract GRWf; the role of operators as observables; the status of non-commutative observables, complementarity, and contextuality.
  6. Concrete definition and construction of GRW theory (1986), with flash (GRWf) or matter density ontology (GRWm); Markovian jump processes in general; stochastic processes in general; relation to the Poisson process; point processes.
  7. Empirical predictions and empirical adequacy of the GRW theories; the two-slit experiment in the GRW theories; how the GRW theories solve the quantum measurement problem; empirical equivalence between GRWf and GRWm. Potential experimental tests of GRW; universal warming.
  8. Bohmian mechanics (1927, 1952): definition, equivariance, empirical predictions. Comparison with GRW theories.
  9. Some toy theories exemplifying the role of the primitive ontology.
  10. The relevance of the primitive ontology; comparison to wave function monism (GRW0); the status of the wave function.
  11. Schrodinger's (1927) and Everett's (1957) many-worlds theories. Comparison with GRW theories.
  12. Trace and partial trace; density matrices; pure and mixed quantum states; statistical and reduced density matrix; decoherence.
  13. The role of density matrices in orthodox quantum theory, GRWf, GRWm, Bohmian mechanics, many-worlds. Conditional wave functions and the status of the wave function.
  14. Properties of the GRW theories: the conditional probability formula, the marginal probability formula, no signalling, invariance under symmetries.
  15. The master equation of GRW theory; Lindblad equations in general; quantum dynamical semi-groups; decoherence; superoperators; the marginal master equation of GRW theory.
  16. The generalized quantum formalism and its derivation from GRWf; the axioms of quantum mechanics as theorems in GRWf. The inexactness involved in the formalism; formalism versus complete theory. Comparison to Bohmian mechanics and many-worlds.
  17. Spin. Nonlocality and Bell's inequality (1964).
  18. Relativity theory. Bohmian mechanics in relativistic space-time.
  19. Relativistic GRWf (2004); relevance of the primitive ontology to relativistic invariance.
  20. The ``free will theorem'' of Conway and Kochen (2006); comparison to relativistic GRWf.
  21. The symmetrization postulate; GRW theory for identical particles according to Dove and Squires (1995); GRW theory for a variable number of particles; Fock space.
  22. Randomness in statistical mechanics, Bohmian mechanics, GRW theories, and many-worlds.