Global Quantization of Vacuum Angle and Magnetic Monopoles as a New Solution to the Strong CP Problem
Abstract
Description
The non-perturbative solution to the strong CP problem with magnetic monopoles as originally proposed by the author is described. It is shown that the gauge orbit space with gauge potentials and gauge tranformations restricted on the space boundary and the globally well-defined gauge subgroup in gauge theories with a $θ$ term has a monopole structure if there is a magnetic monopole in the ordinary space. The Dirac's quantization condition then ensures that the vacuum angle $θ$ in the gauge theories must be quantized to have a well-defined physical wave functional. The quantization rule for $θ$ is derived as $θ=0, 2π/n~(n\neq 0)$ with n being the topological charge of the magnetic monopole. Therefore, the strong CP problem is automatically solved with the existence of a magnetic monopole of charge $\pm 1$ with $θ=\pm 2π$. This is also true when the total magnetic charge of monopoles are very large ($|n|\geq 10^92π$). The fact that the strong CP violation can be only so small or vanishing may be a signal for the existence of magnetic monopoles and the universe is open.
JSUHEP921201, LaTeX 10 pages. To be published in "Fundamental Aspects of Quantum Theory", (World Scientific, Singapore), Proceedings of the International Symposium, Columbia, SC, USA., Dec. 1992)
JSUHEP921201, LaTeX 10 pages. To be published in "Fundamental Aspects of Quantum Theory", (World Scientific, Singapore), Proceedings of the International Symposium, Columbia, SC, USA., Dec. 1992)