# $U(N)$ gauged quantum mechanics

I'm studying the $U(N)$ gauge theory theory in 0+1 dimensions. The aim is to show that this is equivalent to a matrix model. Is there any literature on this topic?

The action I am interested in is

$$S_E = \int d\tau \text{Tr} \left[ \left( D_\tau \Phi \right)^\dagger \left( D_\tau \Phi \right) + m^2 \Phi^\dagger \Phi\right]$$ where $\Phi$ is an adjoint matter field and $S_E$ is the Euclidean action. Also $$D_\tau \Phi = \partial_\tau \Phi + \left[A_\tau, \Phi\right]$$ We gauge fix using $\partial_\tau A_\tau = 0$. I want to be able to describe this system in terms of a matrix model $U \in U(N)$.

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Your action $S_E$ already describes a matrix model (You are using traces....), and this action should be invariant by global transformations $Φ = U Φ U_{-1}, A_{\tau} = U A_{\tau} U_{-1}$, where U, constant, belongs to U(N)\$ –  Trimok May 6 at 7:27