Particles, Astrophysics, and Nuclear Physics Seminar
Quantizing Acceleration Dependent Lagrangians
This will be a general level talk on the quantum mechanics of systems which depend not just on velocity but also on acceleration. Such systems cannot be treated canonically since one quantity (the velocity) cannot serve as a conjugate to two (the position and the acceleration), and have to be quantized using the method of Dirac constraints. The quantization is carried though exactly in a simple model (an oscillator which obeys a fourth order equation of motion rather than a standard second order one), and is shown in general to lead to a Hilbert space with energy eigenstates of negative norm. However, a particular limit of the model is constructed in which none of these negative norm states is then any longer an eigenstate of the Hamiltonian, with the Hamiltonian becoming a defective one in which the number of its eigenstates is less than the number of its eigenvalues.
Monday, November 1, 2004
Gant Science Complex