Reconciling the principles of quantum mechanics with Einsteinian gravitation is one of the major challenges of modern physics.
The Wheeler-DeWitt equation, introduced in the late 1960s, plays a central role in the canonical approach to the problem of quantizing the gravitational field. Somewhat neglected for several decades due to the spectacular success of string theory, which eclipsed it, this equation has recently been the subject of much renewed interest in numerous works devoted to holographic correspondence, the gravitational information problem and quantum cosmology.
The 2024-2025 lecture will establish the Wheeler-DeWitt equation from the Hamiltonian formulation of Einstein's theory, and address the conceptual questions of interpretation that this equation raises. The " problem" of time, subtle in any reparametrization-invariant theory, will be examined in the case of open and closed spaces, where it takes very different forms. The aim of the lecture will be to provide a basis for access to the most recent work. Some of these will be covered in the seminars that will complete the lecture.