Abstract

The gauge principle is the guiding principle of the general program started by Einstein for the geometrization of fundamental interactions. By demanding the invariance of the theory under local coordinate transformations, the relevant fields carrying these interactions appear naturally as non trivial geometrical structures of the corresponding fiber bundles over space-time. In this talk we present a work in progress concerning the study of the geometrical structure and quantization of Yang-Mills theories by using what we have called an extended gauge principle. The three fundamental geometrical components of a Yang-Mills theory -the gauge fields, the gauge fixing and the ghost fieldsare unified in a new geometrical object: an extended connection in a properly chosen principal bundle. In order to construct this extended connection it is necessary to generalize the gauge fixing by using a gauge fixing connection instead of the usual local sections. A fundamental difference is that the gauge fixing connection is globally well defined even when the topology of the fiber bundle is not trivial (Gribov’s obstruction). From the equations for the curvature of the extended connection we derive the corresponding BRST transformations without imposing the usual “flatness” conditions. We show that it is possible to follow the Faddeev-Popov method in order to find the gauge fixed action corresponding to the generalized gauge fixing. 1

Highlights

  • Extended Gauge Principle and Quantization of Gauge TheoriesCP861, Albert Einstein Century International Conference, edited by J.-M

  • The historical importance of General Relativity goes far beyond the fact that it provided a relativistic theory of gravitation

  • The main characteristic of gauge theories is the presence of constraints between the canonical variables. These theories emerge from theories with a global symmetry, which is revealed by the presence of conserved quantities through the first Noether’s theorem

Read more

Summary

Extended Gauge Principle and Quantization of Gauge Theories

CP861, Albert Einstein Century International Conference, edited by J.-M.

INTRODUCTION
THE EXTENDED CONNECTION
BRST SYMMETRY
The extended curvature F has then three components
PATH INTEGRAL QUANTIZATION OF YANG MILLS THEORIES
CONCLUSIONS

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.