Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-05-24
Physics
High Energy Physics
High Energy Physics - Theory
49 pages; v2,3. minor corrections
Scientific paper
We consider an abelian holonomy operator in two-dimensional conformal field theory with zero-mode contributions. The analysis is made possible by use of a geometric-quantization scheme for abelian Chern-Simons theory on $S^1 \times S^1 \times {\bf R}$. We find that a purely zero-mode part of the holonomy operator can be expressed in terms of Riemann's zeta function. We also show that a generalization of linking numbers can be obtained in terms of the vacuum expectation values of the zero-mode holonomy operators. Inspired by mathematical analogies between linking numbers and Legendre symbols, we then apply these results to a space of ${\bf F}_p = {\bf Z}/ p {\bf Z}$ where $p$ is an odd prime number. This enables us to calculate "scattering amplitudes" of identical odd primes in the holonomy formalism. In this framework, the Riemann hypothesis can be interpreted by means of a physically obvious fact, i.e., there is no notion of "scattering" for a single-particle system. Abelian gauge theories described by the zero-mode holonomy operators will be useful for studies on quantum aspects of topology and number theory.
No associations
LandOfFree
Application of abelian holonomy formalism to the elementary theory of numbers does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Application of abelian holonomy formalism to the elementary theory of numbers, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Application of abelian holonomy formalism to the elementary theory of numbers will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-119023