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 \mu m 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 } = 3.8 \cdot 10 ^ { 10 } L _ { \odot } , with their derived star formation rates ranging between 0.2 and 2 M _ { \odot } /yr , with a total of 6.6 M _ { \odot } /yr . None of the typical mid-infrared tracers of AGN activity is detected in either nucleus of the system , excluding the presence of an dust enshrouded accretion disk . 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 \sim 1.6 \cdot 10 ^ { -4 } , similar to that found in many starburst and ULIRGs . The total mass of warm H _ { 2 } in the Antennae is 2.5 \cdot 10 ^ { 7 } M _ { \odot } , with a fraction of warm to total H _ { 2 } gas mass of about 0.35 % . The average warm H _ { 2 } temperature is 302 \pm 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 .