Mastering the master field

Mastering the Master Field∗

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 QCD2. There we both give an explicit construction of the master gauge f...

Considerations: Mastering Data Modeling for Master Data Domains

Mastering Quoridor Mastering Quoridor Mastering Quoridor

OF THESIS Submitted in Partial Fulfillment of the Requirements for the Degree of Bachelor of Science Computer Science The University of New Mexico Albuquerque, New Mexico

The Master Field in Generalised QCD2

As an illustration of the formalism of the master field we consider generalised QCD2. We show how Wilson Loop averages for an arbitrary contour can be computed explicitly and with some ease. A generalised Hopf equation is shown to govern the behaviour of the eigenvalue density of Wilson loops. The collective field description of the theory is therefore deduced. Finally, the non-trivial master g...

On the Master Field in Two Dimensions

A master field is a limiting object in the 1/N expansion of quantum chromodynamics. I give a general introduction to the terminology of quantum field theory. After explaining why the 1/N expansion is reasonable, I describe Singer’s [?] construction of the master field in 2 dimensions. It is followed by a more explicit construction of Gopakumar and Gross [?] (see also [?]). In particular, I expl...