**Joshua Feinberg (Haifa) |** *Solitons and Fluctuations in the Calogero Model * |

Abstract: The collective field formulation of the Calogero model supports periodic density waves. An important set of such density waves is a two-parameter family of BPS solutions of the equations of motion of the collective field theory. One of these parameters is essentially the average particle density, which determines the period, while the other parameter determines the amplitude. We present complete analysis of quadratic fluctuations around these BPS solutions. The corresponding fluctuation hamiltonian (i.e., the stability operator) is diagonalized in terms of bosonic creation and annihilation operators which correspond to the complete orthogonal set of Bloch-Floquet eigenstates of a related periodic Schrodinger hamiltonian, which we derive explicitly. Remarkably, the fluctuation spectrum is independent of the parameter which determines the density wave’s amplitude. As a consequence, the sum over zero-point energies of the field theoretic fluctuation hamiltonian, and its ensuing normal-ordering and regularization, are the same as in the case of fluctuations around constant density background, namely, the ground state. Thus, quadratic fluctuations do not shift the energy density tied with the BPS-density waves studied here, compared to its ground state value. Finally, we also make some brief remarks concerning fluctuations around non-BPS density waves.

When: October 27, 2021 02:00 PM (Jerusalem)

Where: Over Zoom

https://us02web.zoom.us/j/84977047577?pwd=ZWlRKzZnZ2lZc0k2OWxHTWptUjd1Zz09

Meeting ID: 849 7704 7577

Passcode: 725240