Mathematical aspects of the quantum field theory and its applications

2016 Fiscal Year Final Research Report

• Project/Area Number: 15H06453
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Particle/Nuclear/Cosmic ray/Astro physics
• Research Institution: Kagawa University
• Principal Investigator: Fuji Hiroyuki 香川大学, 教育学部, 准教授 (50391719)
• Research Collaborator: Andersen Jørgen Ellegaard ; Penner Robert C. ; Sułkowski Piotr ; Reidys Christian M. ; Manabe Masahide
• Project Period (FY): 2015-08-28 – 2017-03-31
• Keywords: 行列模型 / RNA / 位相的漸化式

Outline of Final Research Achievements

Mathematical aspects of the quantum field theory and its applications to the molecular biology has been studied in this research project. We applied fatgraphs and random matrix model techniques to the geometric study of Ribonucleic Acid (RNA).
The fatgraph is the one dimensional oriented graph utilized widely in geometry, topology, representation theory and quantum field theory. The fatgraph is also useful to describe geometric and topological characterizations of the biohighpolymers such as proteins and RNAs. In this research, we introduced a novel kind of combinatorial parameters referred to "boundary length and point spectrum" which enables us to characterize the secondary structure of RNAs including pseudoknot structures.
We constructed a matrix model for RNAs. Using this model, one can enumerate the number of fatgraphs with the fixed type of the boundary length and point spectrum, and this enumerative model would be useful to understand statistical behaviors in RNA databases.

Free Research Field

数理物理学