Quasi-Exactly-Solvable Many-Body Problems
نویسندگان
چکیده
First known examples of quasi-exactly-solvable N -body problems on the line are presented. These are related to the hidden algebra slN , and they are of two types – containing up to N and up to 6 body interactions only. Both types degenerate to the Calogero model. E-mail: [email protected] E-mail: [email protected] On leave of absence from the Institute for Theoretical and Experimental Physics, Moscow 117259, Russia E-mail: [email protected], [email protected] The Calogero model [1] is one of the most remarkable objects in nonrelativistic multidimensional quantum mechanics. Moreover, a quite exciting relation of this model with to the two-dimensional Yang-Mills theory has been found recently [2]. The Calogero model has many beautiful properties such as: complete-integrability, maximal super-integrability and being an exactly-solvable N -body problem on the real line. The model is defined by the Hamiltonian
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