Speaker
Victor Ovidiu Slupic
("Horia Hulubei" National Institute for R&D in Physics and Nuclear Engineering; Faculty of Physics of the University of Bucharest)
Description
Symmetries commuting with the Hamiltonian explain degeneracies; they do not build spectra. Spectrum generating algebras do: their generators ladder between energy levels, so an entire spectrum is carried by a few irreducible representations. I illustrate the idea where it is cleanest, in the anisotropic harmonic oscillator, whose bilinears in creation and annihilation operators close into the symplectic algebra sp(2n,ℝ) and organize the full Fock space, an analysis with roots in the 1960s. I close with the concept's modern descendants, from the DDF operators of string theory to the SL(2,ℝ) of conformal quantum mechanics.
Author
Victor Ovidiu Slupic
("Horia Hulubei" National Institute for R&D in Physics and Nuclear Engineering; Faculty of Physics of the University of Bucharest)