Basic symplectic geometry for p-branes with thickness in a curved background

Explicit, time-reversible and symplectic integrator for Hamiltonians in isotropic uniformly curved geometries

The kinetic term of the $N$-body Hamiltonian system defined on the surface of the sphere is non-separable. As a result, standard explicit symplectic integrators are inapplicable. We exploit an underlying hierarchy in the structure of the kinetic term to construct an explicit time-reversible symplectic scheme of second order. We use iterative applications of the method to construct a fourth order scheme and demonstrate its efficiency.

Curved String Topology and Tangential Fukaya Categories II

A sequel to arXiv:1111.1460, this paper elaborates on some of the themes in the above paper. Connections to Symplectic Field Theory (SFT) and mirror symmetry are explored.

弯曲时空中的自适应时间步长显式辛积分器

Explicit symplectic integrators with adaptive time steps in curved spacetimes

针对弯曲时空时间变换显式辛积分器难以实现自适应时间步长的问题，团队基于Preto & Saha的步长控制技术开发出自适应版本，其计算成本低、实现简单，能提升模拟效率，可用于研究黑洞混沌动力学等场景。

Continuity of symplectically adjoint maps and the algebraic structure of Hadamard vacuum representations for quantum fields on curved spacetime

We derive for a pair of operators on a symplectic space which are adjoints of each other with respect to the symplectic form (that is, they are sympletically adjoint) that, if they are bounded for some scalar product on the symplectic space dominating the symplectic form, then they are bounded with respect to a one-parametric family of scalar products canonically associated with the initially given one, among them being its ``purification''. As a typical example we consider a scalar field on a globally hyperbolic spacetime governed by the Klein-Gordon equation; the classical system is describe…

Quantum Field Theory on Curved Noncommutative Spacetimes

We summarize our recently proposed approach to quantum field theory on noncommutative curved spacetimes. We make use of the Drinfel'd twist deformed differential geometry of Julius Wess and his group in order to define an action functional for a real scalar field on a twist-deformed time-oriented, connected and globally hyperbolic Lorentzian manifold. The corresponding deformed wave operator admits unique deformed retarded and advanced Green's operators, provided we pose a support condition on the deformation. The solution space of the deformed wave equation is constructed explicitly and can b…

通过余代数和变形Racah代数构造弯曲空间中的超可积系统

Superintegrable systems in curved spaces via coalgebras and deformed Racah algebras

该研究在抽象代数层面推导未变形与非标准q变形𝔰𝔩(2)余代数的泊松代数，构造弯曲空间超可积系统，证明相关恒等式并补充Stäckel模型的最大超可积性。