Matrix generalizations of some dynamic field theories

M. Kardar; A. Zee

doi:10.1016/0550-3213(95)00660-5

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Matrix generalizations of some dynamic field theories

M. Kardar·A. Zee

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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 $N\to\infty$ 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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M. Kardar, A. Zee. 1995-07-25. Matrix generalizations of some dynamic field theories. https://doi.org/10.1016/0550-3213(95)00660-5

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