Many-Particle Models with Two Constants of Interaction

Mikhail Aleksandrovich Braun

A nonrelativistic model is investigated that is a certain generalization of quantum mechanics of two particles interacting with a potential. A new point interaction of the particles is introduced, which involves their transition into another particle that has the same quantum numbers as the bound state of the first particles. In the theory thus developed, the mass of the introduced particle and its interaction constant are arbitrary. In the particular case when the mass of the introduced particle is chosen so that its mass exactly equals that of the bound state of the first particles, the theory is identical with ordinary quantum mechanics. The renormalization constants in this case vanish. (auth)

Sol Wieder

Martin A. Hallnäs, Edwin Langmann A, Cornelius Paufler

As is well known, there exists a four-parameter family of local interactions in 1D. We interpret these parameters as coupling constants of delta-type interactions which include different kinds of momentum-dependent terms, and determine all cases leading to many-body systems of distinguishable particles which are exactly solvable by the coordinate Bethe ansatz. We find two such families of systems, one with two independent coupling constants deforming the well-known delta-interaction model to non-identical particles, and the other with a particular one-parameter combination of the delta and (the so-called) delta-prime interaction. We also find that the model of non-identical particles gives rise to a somewhat unusual solution of the Yang–Baxter relations. For the other model we write down explicit formulae for all eigenfunctions.

Martin Hallnäs, Edwin Langmann A, Cornelius Paufler

As is well known, there exists a four-parameter family of local interactions in 1D. We interpret these parameters as coupling constants of delta-type interactions which include different kinds of momentum-dependent terms, and determine all cases leading to many-body systems of distinguishable particles which are exactly solvable by the coordinate Bethe ansatz. We find two such families of systems, one with two independent coupling constants deforming the well-known delta-interaction model to non-identical particles, and the other with a particular one-parameter combination of the delta and (the so-called) delta-prime interaction. We also find that the model of non-identical particles gives rise to a somewhat unusual solution of the Yang–Baxter relations. For the other model we write down explicit formulae for all eigenfunctions.