arXiv subjects

Taika Okuda

Publications and source records attributed to Taika Okuda.

3 recordsLinked to original sources

arXiv2024

Explicit formula of deformation quantization with separation of variables for complex two-dimensional locally symmetric Kähler manifold

We give a complex two-dimensional noncommutative locally symmetric Kähler manifold via a deformation quantization with separation of variables. We present an explicit formula of its star product by solving the system of recurrence relations given by Hara-Sako. In the two-dimensional case, this system of recurrence relations gives two types of equations corresponding to the two coordinates. From the two types of recurrence relations, symmetrized and antisymmetrized recurrence relations are obtained. The symmetrized one gives the solution of the recurrence relation. From the antisymmetrized one, the identities satisfied by the solution are obtained. The star products for $\mathbb{C}^{2}$ and $\mathbb{C}P^{2}$ are constructed by the method obtained in this study, and we verify that these star products satisfy the identities.

math.DG↗

arXiv2023

Deformation Quantization with Separation of Variables of $G_{2,4}(\mathbb{C})$

We construct a deformation quantization with separation of variables of the Grassmannian $G_{2,4}(\mathbb{C})$. A star product on $G_{2,4}(\mathbb{C})$ can be explicitly determined as the solution of the recurrence relations for $G_{2,4}(\mathbb{C})$ given by Hara and one of the authors (A. Sako). To provide the solution to the recurrence relations, it is necessary to solve a system of linear equations in each order. However, to give a concrete expression of the general term is not simple because the variables increase with the order of the differentiation of the star product. For this reason, there has been no formula to express the general term of the recurrence relations. In this paper, we overcome this problem by transforming the recurrence relations into simpler ones. We solve the recurrence relations using creation and annihilation operators on a Fock space. From this solution, we obtain an explicit formula of a star product with separation of variables on $G_{2,4}(\mathbb{C})$.

math-ph↗

arXiv2017

Asymptotically flat multi-black lenses

We present an asymptotically flat and stationary multi-black lens solution with bi-axisymmetry of $U(1)\times U(1)$ as a supersymmetric solution in the five-dimensional minimal ungauged supergravity. We show that the spatial cross section of each degenerate Killing horizon admits different lens space topologies of $L(n,1)=S^3/{\mathbb Z_n}$ as well as a sphere $S^3$. Moreover, we show that in contrast to the higher dimensional Majumdar-Papapertrou multi-black hole and multi-BMPV black hole spacetimes, the metric is smooth on each horizon even if the horizon topology is spherical.

hep-th↗