Lecture Series with Systematic Expositions
This page collects together the lectures series given by the author on quantum mechanics and quantum cosmology. These are as close to a systematic exposition as the author has managed to get. They have been referred to on other pages in specific contexts. Here they are collected together. The latest is from 2008.
Spacetime Quantum Mechanics and the Quantum Mechanics of Spacetime, Lectures at the 1992 Les Houches Summer School, Gravitation and Quantizations [107,GQMST].
The central objective of these lectures is a sum-over-histories generalized quantum mechanics (GQMST) for spacetime geometry and matter fields that is in fully spacetime form and therefore adequate for prediction in quantum cosmology. In particular, this formulation can be used to justify the rules that are used to derive the probabilities for the possible classical spacetimes predicted by a quantum state of the universe in the semiclassical approximation. This generalization of usual quantum theory underlies, at least implicitly, all of the predictions made in the other papers on this site.
Along the way decoherent histories quantum mechanics of closed systems such as the universe is reviewed. The principles of generalized quantum mechanics are introduced and illustrated by applications to abelian gauge theories and the single relativistic world line. It's shown how GQMST is free from any problem of time and how usual quantum mechanics with its preferred notions of time is recovered when spacetime geometry behaves classically with high probability.
The author intended to put make the material in this long document more accessible in a series of papers. Unfortunately, it remains the only exposition of this way of formulating the quantum mechanics of cosmology as far as the author is aware. A reader might be helped by first reading
the summary at end of the lectures here [GQMSTsum] or a précis of the lectures [123].
The Quantum Mechanics of Cosmology, lectures at the 1989 Jerusalem Winter School for Theoretical Physics, Quantum Cosmology and Baby Universes [91]
An exposition of decoherent histories quantum mechanics in the context of quantum cosmology. (The term ``post-Everett quantum mechanics'' used here that was intended to recognize Everett did not catch on.) Copenhagen quantum mechanics as an approximation appropriate to measurement situations is explicitly discussed. So is the connection with reduced density matrices. Generalized quantum mechanics is introduced. Its use in formulating quantum theory with spacetime regions, closed timelike curves, and non-trivial time topology is discussed. The construction of a generalized quantum mechanics of spacetime geometry is started.
Prediction in Quantum Cosmology, lectures at the 1986 Cargèse Summer School on Gravitation in Astrophysics [77]
An early introduction to the process of prediction in quantum cosmology. The general issues discussed are still current. But the specific formulation of quantum theory has been superseded by more recent work (e.g. [107]). What still may be of interest is the review of the derivation of quantum field theory in curved spacetime from the Wheeler-DeWitt as the analog of the Born-Oppenheimer approximation, and the derivation of the Bunch-Davies vacuum from the no-boundary wave function of the universe.
Quantum Cosmology, lectures at the Theoretical Advanced Study Institute in Elementary Particle Physics (TASI), Yale University, 1985 [70]
An early introduction to quantum cosmology stressing the observational importance of a theory of the quantum initial condition of the universe as as part of the fundamental laws of physics. Histories are emphasized, but these are before decoherent histories quantum theory was formulated. The no-boundary wave function is described (although not called this), the constraints it satisfies derived, and its consequences for linearized gravity and field theory in curved spacetime discussed. Probably mostly of historical interest.
Quantum Mechanics in the Light of Quantum Cosmology, Videos of two Lectures at the University of Michigan Quantum Summer School. June 26-27, 2007. (the sound quality is not very good) [Lect1, Lect2]
Two elementary chalkboard lectures on decoherent histories quantum theory aimed at beginning graduate students.