Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-11-03
Nucl.Phys. B451 (1995) 379-415
Physics
High Energy Physics
High Energy Physics - Theory
46 pages plus 11 uuencoded eps figures
Scientific paper
10.1016/0550-3213(95)00340-X
The basic concepts of non-commutative probability theory are reviewed and applied to the large $N$ limit of matrix models. We argue that this is the appropriate framework for constructing the master field in terms of which large $N$ theories can be written. We explicitly construct the master field in a number of cases including QCD$_2$. There we both give an explicit construction of the master gauge field and construct master loop operators as well. Most important we extend these techniques to deal with the general matrix model, in which the matrices do not have independent distributions and are coupled. We can thus construct the master field for any matrix model, in a well defined Hilbert space, generated by a collection of creation and annihilation operators---one for each matrix variable---satisfying the Cuntz algebra. We also discuss the equations of motion obeyed by the master field.
Gopakumar Rajesh
Gross David J.
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