Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-03-07
Mod.Phys.Lett. A10 (1995) 2323-2334
Physics
High Energy Physics
High Energy Physics - Theory
10 pages, LaTex
Scientific paper
10.1142/S0217732395002489
In recent works by Singer, Douglas and Gopakumar and Gross an application of results of Voiculescu from non-commutative probability theory to constructions of the master field for large $N$ matrix field theories have been suggested. In this note we consider interrelations between the master field and quantum groups. We define the master field algebra and observe that it is isomorphic to the algebra of functions on the quantum group $SU_q(2)$ for $q=0$. The master field becomes a central element of the quantum group Hopf algebra. The quantum Haar measure on the $SU_q(2)$ for any $q$ gives the Wigner semicircle distribution for the master field. Coherent states on $SU_q(2)$ become coherent states in the master field theory.
Accardi Luigi
Aref'eva Irina Ya.
Kozyrev S. V.
Volovich Igor V.
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