Fourier Transform Question - Negative Frequencies?

[J$C]

When I see a graph of a Fourier Transform, or something in the frequency domain, say band-limited from -\Omega to \Omega, I'm confused to what the interpretation is of the negative frequencies. Physically it would seem as though something considered in cycles/second for example, should be positive but mathematically the FT will allow for negative frequencies.

Can somebody clarify this for me?

 

[HallsofIvy]

e^{-\omega ix}= e^{\omega (-i)x} so negative frequencies are just the complex conjugate of the positive frequencies.

 

[Phrak]

Hadn't really thought about it. Physically positive/negative frequencies could be interpreted as left/right circularly polarized waves.