Mode-sum construction of the two-point functions for the Stueckelberg vector fields in the Poincaré patch of de Sitter space

Abstract

We perform canonical quantization of the Stueckelberg Lagrangian for massive vector fields in the conformally flat patch of de Sitter space in the Bunch-Davies vacuum and find their Wightman two-point functions by the mode-sum method. We discuss the zero-mass limit of these two-point functions and their limits where the Stueckelberg parameter $\xi$ tends to zero or infinity. It is shown that our results reproduce the standard flat-space propagator in the appropriate limit. We also point out that the classic work of Allen and Jacobson for the two-point function of the Proca field and a recent work by Tsamis and Woodard for that of the transverse vector field are two limits of our two-point function, one for $\xi \to \infty$ and the other for $\xi \to 0$. Thus, these two works are consistent with each other, contrary to the claim by the latter authors.

23 pages, matches published version

References in corpus (10)

• Stochastic Inflationary Scalar Electrodynamics
• The IR stability of de Sitter: Loop corrections to scalar propagators
• Two loop stress-energy tensor for inflationary scalar electrodynamics
• Two Loop Scalar Bilinears for Inflationary SQED
• Loops in inflationary correlation functions
• One-loop gravitational wave spectrum in de Sitter spacetime
• A Maximally Symmetric Vector Propagator
• One Loop Corrected Mode Functions for SQED during Inflation
• Infrared behavior and gauge artifacts in de Sitter spacetime: The photon field
• QFT in the flat chart of de Sitter space

Cited by in corpus (24)

• Graviton Loop Corrections to Vacuum Polarization in de Sitter in a General Covariant Gauge
• Mode-sum construction of the covariant graviton two-point function in the Poincaré patch of de Sitter space
• Adiabatic Regularization for Gauge Field and the Conformal Anomaly
• Stueckelberg massive electromagnetism in curved spacetime: Hadamard renormalization of the stress-energy tensor and the Casimir effect
• Stueckelberg massive electromagnetism in de Sitter and anti-de Sitter spacetimes: Two-point functions and renormalized stress-energy tensors
• Propagators for gauge-invariant observables in cosmology
• Electromagnetic field correlators and the Casimir effect for planar boundaries in AdS spacetime with application in braneworlds
• Even the photon propagator must break de Sitter symmetry
• Removing the Faddeev-Popov zero modes from Yang-Mills theory in spacetimes with compact spatial sections
• Relative Entropy in de Sitter is a Noether Charge
• Abelian Higgs model in power-law inflation: the propagators in the unitary gauge
• Electromagnetic vacuum fluctuations around a cosmic string in de Sitter spacetime
• Electromagnetic Casimir densities for a cylindrical shell on de Sitter space
• Which part of the stress-energy tensor gravitates?
• Photon propagator for inflation in the general covariant gauge
• Large-distance behaviour of the massless vector two-point function in de Sitter spacetime
• Propagators in curved spacetimes from operator theory
• Photon quantization in cosmological spaces
• Regularized stress tensor of vector fields in de Sitter space
• Gauge dependence in QED amplitudes in expanding de Sitter space
• Maxwell field with gauge fixing term in the radiation- and matter-dominant stages: exact solution and stress tensor
• Majorana propagator on de Sitter space
• Inflation and late time acceleration designed by Stueckelberg massive photon
• Electromagnetic vacuum stresses and energy fluxes induced by a cosmic string in de Sitter spacetime