Quantum field theory and the connected differential geometry

点击翻译按钮获取中文摘要

The subjects : The subjects are devided into two parts :(1) Hermitian Hurwitz pairs and the sgnature problems of the space-time(2) Divergence problems in quantum field theory and the Riemann-Hilbert problemsThe results(1) Hermitian Hurwitz pairs state some restriction on the sgnatures of the pseudo-Euclidean space. This leads us to the research on the sgnature problems of the space time. By use of the duality theorems, we consider the problem of 4 dimensional space-time. We obtain : (1,3) -space is equivalent to (2,2) -space by the Hurwitz duality and (1,3) -space is equivalent to (3,1) -space by use of the space-time duality. Hence, we have the only one space-time for 4-spaces.(2) Divergences appear in the quantum field theory very often. We consider the geometry of divergence by use of the Riemann-Hilbent problems. The regular singularities are very important candidate, because of its closeduess and the relation to the Green komel. We formulate the quantum version of the R.-H.problem and solve it. We notice its expectation value becomes functions with regular singularities