Quantum Yang-Mills theory in de Sitter ambient space formalism

Abstract

We present the quantum Yang-Mills theory in the four-dimensional de Sitter ambient space formalism. In accordance with the SU$(3)$ gauge symmetry the interaction Lagrangian is formulated in terms of interacting color charged fields in curved space-time. The gauge-invariant field equations are obtained in an independent coordinate description, and their corresponding color conserved currents are computed. Faddeev-Popov ghost fields are shown to be equivalent to their Minkowski counterparts. We obtain that the free ghost fields are massless minimally coupled scalar fields. The problems of the vacuum state, namely the breaking of de Sitter invariance, and the appearance of infrared divergence in its quantization procedure, are discussed. The existence of an axiomatic quantum Yang-Mills theory within the framework of the Krein space quantization is examined. The infrared divergence regularization of the interaction between the gauge vector fields and the ghost fields is studied in the one-loop approximation. Two different regularization methods are discussed: cut-off regularization and Krein space regularization. A mass term for the gauge vector fields is obtained, which may explain the mass gap and the color confinement problems at the quantum level in de Sitter background. The large curvature limit at the early universe or inflationary epoch is considered.

arXiv comment19 pages, some references added, two appendices added, explanations added, typos corrected

References in corpus (22)

• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Two-point Functions and Quantum Fields in de Sitter Universe
• Geodesic equation in Schwarzschild--(anti-)de Sitter space--times: Analytical solutions and applications
• Gupta-Bleuler quantization for minimally coupled scalar fields in de Sitter space
• Lightcone fluctuations in flat spacetimes with nontrivial topology
• Massive Spin-2 Field in De Sitter Space
• "Massless" vector field in de Sitter Universe
• "Massive" vector field in de Sitter space
• One-loop effective action around de Sitter space
• Casimir Effect In Krein Space Quantization
• Krein space quantization in curved and flat spacetimes
• QED effective action in Krein space quantization
• Krein Regularization of QED
• Super-gauge Field in de Sitter Universe
• Confinement of spinless particles by Coulomb potentials in two-dimensional space-time
• Abelian Gauge Theory in de Sitter Space
• Covariant Quantization of "Massive" Spin-3/2 Fields in the de Sitter Space
• Gupta-Bleuler quantization for linearized gravity in de Sitter spacetime
• "Massive" Rarita-Schwinger field in de Sitter space
• "Krein" regularization method
• Polarization tensor in de Sitter gauge gravity
• Infrared problem in the Faddeev-Popov-ghost propagator in perturbative quantum gravity in de Sitter spacetime

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• Scalar and vector gauges unification in de Sitter ambient space formalism
• Axiomatic de Sitter quantum Yang-Mills theory with color confinement and mass gap
• Quantum de Sitter geometry
• Krein space quantization and New Quantum Algorithms
• Krein Space Quantization and a Spectral Interpretation of the Riemann $\xi$-Function