Invited chapter contribution submitted to arXiv

This is mainly based on some part of the previous paper. I have submitted to the category of math.AP (Analysis of PDEs) for the first time. Since one cannot make a submission to a new category without an endorsement, I have asked a mathematician who would edit the book for a favor. For details, please refer to here.

Add "Essay" to the item of Memoirs

The essay is written in Japanese in a blog style.

Nair's Lecture Notes, second draft

I have left this draft for a long time. The second version is here. Materials that have been added and revised by Prof. Nair long before are also included in this version. Please let me know if there are any typos or corrections.

Particle data updated

Particle data screening system is revised with the latest set of data from Particle Data Group. The revised version is here. The total number of listed particles rises from 212 to 214, adding two new particles, K(0)*(700) and Delta(1900). The charges of these are (0,+) and (-,0,+,++), respectively. There are also two renamed particles, which are chi(c2)(2P) --> chi(c2)(3930) and Upsilon(1D) --> Upsilon(2)(1D).

Paper submitted to arXiv

Motivated by the previous result that a holomorphic zero-mode wave function in abelian Chern-Simons theory on the torus can be considered as a quantum version of a modular form of weight 2, we consider how a Hecke operator acts on such wave functions. We argue that the action of the Hecke operator can be considered as a sum over possible gauge transformations of the wave function. (The gauge transformations are induced by doubly periodic translations.) The resultant expressions suggest that the notion of the level which is inherent to the modular forms naturally arises for the wave function. We also present a speculative idea on the computation of the Hecke eigenvalues. I have tried to find more fruitful results but spent a few months in vain. For details please see the paper.