We derive the basic canonical brackets amongst the creation and annihilation operators for a two (1 + 1)-dimensional (2D) gauge field theoretic model of an interacting Hodge theory where a U(1) gauge field (A_μ) is coupled with the fermionic Dirac fields (ψand \bar ψ). In this derivation, we exploit the spin-statistics theorem, normal ordering and the strength of the underlying six infinitesimal continuous symmetries (and the concept of their generators) that are present in the theory. We do not use the definition of the canonical conjugate momenta (corresponding to the basic fields of the theory) anywhere in our whole discussion. Thus, we conjecture that our present approach provides an alternative to the canonical method of quantization for a class of gauge field theories that are physical examples of Hodge theory where the continuous symmetries (and corresponding generators) provide the physical realizations of the de Rham cohomological operators of differential geometry at the algebraic level.
Triple Hodge integrals and constant Poisson brackets for rank-one Dubrovin-Zhang hierarchies
Korteweg–de Vriesinstituut voor Wiskunde, Universiteit van Amsterdam（阿姆斯特丹大学科特韦格-德弗里斯数学研究所）；Université Bourgogne Europe, CNRS, IMB UMR 5584（勃艮第欧洲大学，法国国家科学研究中心，IMB UMR 5584）
Asymptotic limits in class-$\mathcal{S}$ theories and non-Abelian Hodge theory
Center of Mathematical Sciences and Applications, Harvard University（哈佛大学数学科学与工程应用中心）；Institute for Theoretical Physics, Utrecht University（乌得勒支大学理论物理研究所）；Jefferson Physical Laboratory, Harvard University（哈佛大学杰斐逊物理实验室）
On Calabi-Yau Complete Intersections in Toric Varieties
研究了$d$维环面Fano簇中$r$半样本因子的Calabi-Yau完全交$V$的Hodge理论性质.我们的主要目的是证明第二作者提出的组合对偶与镜像对称预言的Hodge数的对偶是一致的。预计对任意维度奇异卡-丘变体$V$的镜像对称预测的完整验证需要考虑所谓的{ \em弦理论霍奇数} $h^{p,q}_{\rm st}(V)$。我们仅限于弦理论霍奇数$h^{0,q}_{\rm st}(V)$和$h^{1,q}_{\rm st}(V)$ $(0 \leq q \leq d-r) which coincide with the usual Hodge numbers $ h^{0，q}（\widehat{V}）$ and $ h^{1，q}（\widehat{V}）$ of a $ MPCP $-desingularization $ \widehat{V} $ of $ V$。
