Path-integral evaluation of the time-evolution propagator for quadratic Hamiltonian systems with application to the Lee model
Abstract
Path integral methods are used to derive an exact expression for the time evolution propagator for a broad class of systems with quadratic Hamiltonians. For a certain sub-class of such systems, the result is reduced to a simplified closed form. The propagators are exhibited for several illustrative elementary cases and for the Lee model for a single heavy particle, with two isotopic states of equal mass, interacting with a bosonic field. The propagator for the latter is used to calculate the survival probability of the unstable state of the heavy particle with no bosons present.
- Publication:
-
Ph.D. Thesis
- Pub Date:
- September 1974
- Bibcode:
- 1974PhDT........29P
- Keywords:
-
- Hamiltonian Functions;
- Nuclear Models;
- Particle Interactions;
- Boson Fields;
- Particle Trajectories;
- Quadratic Equations;
- Theoretical Physics;
- Atomic and Molecular Physics