We present an analysis of the kinematics and excitation of the warm ionized gas in two obscured, powerful quasars at z>=3.5 from the SWIRE survey, SWIRE J022513.90-043419.9 and SWIRE J022550.67-042142, based on imaging spectroscopy on the VLT. Line ratios in both targets are consistent with luminous narrow-line regions of AGN. SWIRE J022550.67-042142 has very broad (FWHM=2000 km/s), spatially compact [OIII] line emission. SWIRE J022513.90-043419.9 is spatially resolved, has complex line profiles of H-beta and [OIII], including broad wings with blueshifts of up to -1500 km/s relative to the narrow [OIII]5007 component, and widths of up to FWHM=5000 km/s. Estimating the systemic redshift from the narrow H-beta line, as is standard for AGN host galaxies, implies that a significant fraction of the molecular gas is blueshifted by up to ~ -1000 km/s relative to the systemic velocity. Thus the molecular gas could be participating in the outflow. Significant fractions of the ionized and molecular gas reach velocities greater than the escape velocity. We compare empirical and modeling constraints for different energy injection mechanisms, such as merging, star formation, and momentum-driven AGN winds. We argue that the radio source is the most likely culprit, in spite of the sources rather modest radio power of 10^25 W/Hz. Such a radio power is not uncommon for intense starburst galaxies at z~2. We discuss these results in light of the co-evolution of AGN and their host galaxy.
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