Matrix generalizations of some dynamic field theories
M. Kardar, A. Zee
Abstract
We introduce matrix generalizations of the Navier--Stokes (NS) equation for fluid flow, and the Kardar--Parisi--Zhang (KPZ) equation for interface growth. The underlying field, velocity for the NS equation, or the height in the case of KPZ, is promoted to a matrix that transforms as the adjoint representation of SU(N). Perturbative expansions simplify in the N∞ limit, dominated by planar graphs. We provide the results of a one--loop analysis, but have not succeeded in finding the full solution of the theory in this limit.
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