Solvable Matrix Models
نویسنده
چکیده
We review some old and new methods of reduction of the number of degrees of freedom from ∼ N 2 to ∼ N in the multi-matrix integrals.
منابع مشابه
On Algebraic Classiication of Quasi-exactly Solvable Matrix Models
We suggest a generalization of the Lie algebraic approach for constructing quasi-exactly solvable one-dimensional Schrr odinger equations which is due to Shifman and Turbiner in order to include into consideration matrix models. This generalization is based on representations of Lie algebras by rst-order matrix diierential operators. We have classiied inequivalent representations of the Lie alg...
متن کاملOn algebraic classification of quasi-exactly solvable matrix models
We suggest a generalization of the Lie algebraic approach for constructing quasi-exactly solvable one-dimensional Schrödinger equations which is due to Shifman and Turbiner in order to include into consideration matrix models. This generalization is based on representations of Lie algebras by first-order matrix differential operators. We have classified inequivalent representations of the Lie a...
متن کاملv 1 1 0 O ct 1 99 5 Quasi - exactly solvable problems and random matrix theory
There exists an exact relationship between the quasi-exactly solvable problems of quantum mechanics and models of square and rectangular random complex matrices. This relationship enables one to reduce the problem of constructing topological (1/N) expansions in random matrix models to the problem of constructing semiclassical expansions for observ-ables in quasi-exactly solvable problems. Lie a...
متن کاملExactly Solvable Three-body SUSY Systems with Internal Degrees of Freedom
The approach of multi-dimensional SUSY Quantum Mechanics is used in an explicit construction of exactly solvable 3-body ( and quasi-exactly-solvable N -body ) matrix problems on a line. From intertwining relations with time-dependent operators, we build exactly solvable non-stationary scalar and 2 × 2 matrix 3-body models which are time-dependent extensions of the Calogero model. Finally, we in...
متن کاملMatrix Models as Solvable Glass Models Typeset Using Revt E X
We present a family of solvable models of interacting particles in high di-mensionalities without quenched disorder. We show that the models have a glassy regime with aging eeects. The interaction is controlled by a parameter p. For p = 2 we obtain matrix models and for p > 2 `tensor' models. We concentrate on the cases p = 2 which we study analytically and numerically.
متن کاملX iv : h ep - t h / 98 10 04 5 v 1 7 O ct 1 99 8 TPI - MINN - 98 / 04 Quasi - Exactly Solvable Models with Spin - Orbital Interaction
First examples of quasi-exactly solvable models describing spin-orbital interaction are constructed. In contrast with other examples of matrix quasi-exactly solvable models discussed in the literature up to now, our models admit infinite (but still incomplete) sets of exact (algebraic) solutions. The hamiltonians of these models are hermitian operators of the form H = −∆ +V1(r)+ (s · l)V2(r)+ (...
متن کامل