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A Hamiltonian formulation for the Grosse-Wulkenhaar $\phi^{4}_{\star D}$model is performed. The study is based on $D+1$ dimensional space-timeformulation of $D$ dimensional non-local theories. The analysis of constraintsshows that the secondary constraints describe the Euler-Lagrange equations ofmotion. Relevant tensors are computed and analyzed.

Hamiltonian formulation of the Grosse-Wulkenhaar $\phi^{4}_{\star D}$ model