We study the collective field formulation of a restricted form of the multi-species Calogero model, in which the three-body interactions are set to zero. We show that the resulting collective field theory is invariant under certain duality transformations, which interchange, among other things, particles and antiparticles, and thus generalize the well known strong-weak coupling duality symmetry of the ordinary Calogero model. We identify all these dualities, which form an Abelian group, and study their consequences. We also study the ground state and small fluctuations around it in detail, starting with the two-species model, and then generalizing to an arbitrary number of species.
Bibliographical noteFunding Information:
This work was supported by the Ministry of Science and Technology of the Republic of Croatia under contract No. 0098003. J.F. wishes to thank the Center for Nonlinear Studies at the Los Alamos National Laboratory, and in particular, Carl Bender and Bob Ecke, for the kind hospitality extended to him during the completion of this work.
- Collective-field theory
- Multi-species Calogero model
ASJC Scopus subject areas
- Nuclear and High Energy Physics