  Using the Infrared Spectrograph on the Spitzer Space Telescope, we observed
the Antennae galaxies obtaining spectral maps of the entire central region and
high signal-to-noise 5-38 um spectra of the two galactic nuclei and six
infrared-luminous regions. The total infrared luminosity of our six IR peaks
plus the two nuclei is L_IR = 3.8x10^10 L_o, with their derived star formation
rates ranging between 0.2 and 2 M_o/yr, with a total of 6.6 M_o/yr. The hardest
and most luminous radiation originates from two compact clusters in the
southern part of the overlap region, which also have the highest dust
temperatures. PAH emission and other tracers of softer radiation are spatially
extended throughout and beyond the overlap region, but regions with harder and
intenser radiation field show a reduced PAH strength. The strong H_2 emission
is rather confined around the nucleus of NGC 4039, where shocks appear to be
the dominant excitation mechanism, and the southern part of the overlap region,
where it traces the most recent starburst activity. The luminosity ratio
between the warm molecular gas (traced by the H_2 lines) and the total far-IR
emission is ~1.6x10^-4, similar to that found in many starburst and ULIRGs. The
total mass of warm H_2 in the Antennae is 2.5x10^7 M_o, with a fraction of warm
to total H_2 gas mass of about 0.35%. The average warm H_2 temperature is
302+/-26 K and appears anti-correlated with the radiation field hardness,
possibly due to an evolution of the PDR morphology. The previously reported
tight correlation between the H_2 and PAH emission was not found but higher
total PAH emission to continuum ratios were found in PDRs with warmer gas.
