Perturbations of unitary representations of finite dimensional Lie groups
- Department of Physics, Grinnell College, Grinnell, IA 50112 (United States)
In quantum physical theories, interactions in a system of particles are commonly understood as perturbations to certain observables, including the Hamiltonian, of the corresponding interaction-free system. The manner in which observables undergo perturbations is subject to constraints imposed by the overall symmetries that the interacting system is expected to obey. Primary among these are the spacetime symmetries encoded by the unitary representations of the Galilei group and Poincare group for the non-relativistic and relativistic systems, respectively. In this light, interactions can be more generally viewed as perturbations to unitary representations of connected Lie groups, including the non-compact groups of spacetime symmetry transformations. In this paper, we present a simple systematic procedure for introducing perturbations to (infinite dimensional) unitary representations of finite dimensional connected Lie groups. We discuss applications to relativistic and non-relativistic particle systems.
- OSTI ID:
- 21336072
- Journal Information:
- Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 12 Vol. 324; ISSN 0003-4916; ISSN APNYA6
- Country of Publication:
- United States
- Language:
- English
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