MR2065946 Grosse, Harald ; Langmann, Edwin ; Paufler, Cornelius .
Exact solution of a 1D quantum many-body system with
momentum-dependent interactions. J. Phys. A 37 (2004), no. 16,
4579--4592.



The main appeal of the point (most often: delta-function-like)
interactions lies in the related simplified (viz., matching)
technique of construction of the solutions of the underlying
Schroedinger equation. A particular derivative-coupling model of
this type is proposed. The model and its mapping to the 1D boson
gas exhibit a limiting-transition connection to the famous massive
Thirring model and to its well known duality to the sine-Gordon
model. Unfortunately, a declared generalization of the latter
duality proved erroneous (see the corrigendum published on p. 6855
of the same journal volume, and MR 2076 472).


MR2076472 Grosse, H. ; Langmann, E. ; Paufler, C. Corrigendum:
“Exact solution of a 1D many-body system with momentum-dependent
interactions“ [J. Phys. A 37 (2004), no. 16, 4579--4592;
MR2065946]. J. Phys. A 37 (2004), no. 26, 6855.


In a way falsifying the statements on duality involving ARBITRARY
exchange statistics in the model proposed on pp. 4579 - 4592 of
the same journal volume (cf. also MR 2065 946), the authors report
the existence of a three-body counterexample where certain
consistency requirements prove fulfilled only for bosons or
fermions. Then, their use of the coordinate Bethe ansatz is
explained NOT to imply the originally declared exact solvability
of their model.

81Q05 35C05  35J10  35Q40  82B23