Abstract
We introduce the 3-colour noncommutative quantum field theory model in two dimensions. For this model we prove a generalised Ward–Takahashi identity, which is special to coloured noncommutative QFT models. It reduces to the usual Ward–Takahashi identity in a particular case. The Ward–Takahashi identity is used to simplify the Schwinger–Dyson equations for the 2-point function and the N-point function. The absence of any renormalisation conditions in the large (mathcal {N},V)-limit in 2D leads to a recursive integral equation for the 2-point function, which we solve perturbatively to sixth order in the coupling constant.
Highlights
Consider a hexagonal lattice with three different coloured links, where at each vertex all three links carry different colours
We introduce the 3-colour noncommutative quantum field theory model in two dimensions
The absence of any renormalisation conditions in the large (N, V )-limit in 2D leads to a recursive integral equation for the 2-point function, which we solve perturbatively to sixth order in the coupling constant
Summary
Consider a hexagonal lattice with three different coloured links, where at each vertex all three links carry different colours. Two-dimensional quantum gravity can be formulated as a counting problem for triangulations of random surfaces, which leads to the connection between 2D quantum gravity and random matrices [4,5] It was proved by Kontsevich [6] that the solution of an action of the form tr(E. In this paper we will study the noncommutative 3-colour model as a quantum field theoretical model Speaking, it is the model solved by Kostov with an additional external dynamical field E of linearly-spaced eigenvalues. It is the model solved by Kostov with an additional external dynamical field E of linearly-spaced eigenvalues It shares topologically some graphs with the noncommutative 3-model [14], it has more similarities to the. The linear and discrete dependence of Em reflects the eigenvalue spectrum of the quantum-mechanical harmonic oscillator
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