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We construct the deformation quantization with separation of variables on theGrassmannian $G_{2,4}\left(\mathbb{C}\right)$. The star product on$G_{2,4}\left(\mathbb{C}\right)$ can be explicitly determined as the solutionof the recurrence relations for $G_{2,4}\left(\mathbb{C}\right)$ given by Haraand one of the authors (A. S.). To give the solution of the recurrencerelations, it is necessary to solve a system of linear equations at each order.However, to give the concrete expression of the general term is not easybecause the variables increase with the order of the differentiation of thestar product. For this reason, there has been no formula to express the generalterm of the recurrence relations. In this paper, by overcoming this problem bytransforming the recurrence relations into simpler ones, we obtain the formulafor the general term. We solve the recurrence relations by using creation andannihilation operators on a Fock space. From this solution, we obtain theexplicit formula of the star product with separation of variables on$G_{2,4}\left(\mathbb{C}\right)$.

Deformation quantization with separation of variables of $G_{2,4}\left(\mathbb{C}\right)$