The many-body problem in terms of particle group functions

L. Szasz

G A Kerimov

The class of one-dimensional many-body systems related to semisimple Lie groups G is studied. The Hamiltonians of these systems are expressed in terms of Casimir operators (or, equivalently, Laplace-Beltrami operators on symmetric spaces) of underlying symmetry groups G . It turns out that the S matrix for all these problems is related to the intertwining operators for groups G . This connection provides immediately the functional form of the S matrix. Moreover, this connection allows one to prove that multiparticle S -matrix elements can be expressed in terms of two-particle ones.

Ricardo A. Broglia

N. H. March, William H. L. Young, S. Sampanthar +1 more

J R Armstrong, Artem G. Volosniev, D V Fedorov +2 more

We describe a procedure to solve an up to problem where the particles are separated topologically in N groups with at most two particles in each. Arbitrary interactions are allowed between the (two) particles within one group. All other interactions are approximated by harmonic oscillator potentials. The problem is first reduced to an analytically solvable N -body problem and N independent two-body problems. We calculate analytically spectra, wave functions, and normal modes for both the inverse square and delta-function two-body interactions. In particular, we calculate separation energies between two strings of particles. We find that the string separation energy increases with N and interaction strength.