Sometimes research doesn't go well. Other times, it really doesn't go well. And sometimes, it's a veritable dumpsterfire. I've slid through all three of these stages this quarter and my project doesn't seem to be relenting any time soon.
The most frustrating part of it all is that, just by looking at the integral I'm wrestling with, I know I should be able to compute it. I know the answer, I know the integrand is well behaved (in most places at least), and I know for sure that people have done it before. But calculating this thing is like baking a soufflé: if anything is done even slightly incorrectly, you're gonna have one floppy, deflated pastry. And nobody wants that.
One thing I have learned from all this struggling however is that I have a good support system. I've of course been complaining to my family and friends whenever I've gotten the chance, but I've also received help from various group members, both previous and current. The integral is inadvertently teaching me an enormous amount of many-body physics, UEG stuff, a dash of perturbation theory, and more than I'd care to know about Fourier transforms so even struggles are, I suppose, time well spent (though often it doesn't feel like it). Regardless of the future research I do with this thing, it's been a hell of a teaching tool.
I just hope that the finite-temperature form isn't too much worse...