Gauge theories: geometry and cohomological invariants

DOI10.1023/A:1026688407799zbMATH Open0969.53011arXivhep-th/9707106OpenAlexW1565944517MaRDI QIDQ1303441

V. Pereyra

Publication date: 1 December 1999

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

Abstract: We develop a geometrical structure of the manifolds $Gamma$ and $hatGamma$ associated respectively to the gauge symmetry and to the BRST symmetry. Then, we show that ($hatGamma,hatzeta,Gamma$), where $hatzeta$ is the group of BRST transformations, is endowed with the structure of a principle fiber bundle over the base manifold $Gamma$. Furthermore, in this geometrical set up due to the nilpotency of the BRST operator, we prove that the effective action of a gauge theory is a BRST-exact term up to the classical action. Then, we conclude that the effective action where only the gauge symmetry is fixed, is cohomologically equivalent to the action where the gauge and the BRST symmetries are fixed.

Full work available at URL: https://arxiv.org/abs/hep-th/9707106

zbMATH Keywords

gauge symmetrygauge theoryBRST symmetryprincipal fiber bundle

Mathematics Subject Classification ID

Yang-Mills and other gauge theories in quantum field theory (81T13) Quantization in field theory; cohomological methods (81T70) Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07)

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