September 7, 2006

vacuuming nightmare

in quantum field theory, in the process of making calculations, there often arise situations where you can only deal with the energy difference between two states, and you ignore what an "abosolute" energy would be. in the context of understanding the Lagrangian you are working on, this doesn't cause any difficulties, but overall that supposedly meaningless absolute energy eventually becomes offset, so to speak, by the accumulation of these energy differences. it turns out that you can actually find out what all these offsets are and add them up to see the individual energy terms of every particle interaction. most of these are are "vacuum energy" terms which come into consideration only in certain situations, such as the cosmological constant problem as a potential source of missing energy (though it's too small).

well, a physicist with a sense of humor went through the trouble of finding this abomination, and making it into a pdf. in fact, he even proposes an exam question based on it!

exercise given locality, causality, lorentz invariance, and known physical data since 1860, show that the lagrangian describing all observed physical processes (sans gravity) can be written:

brilliant! i think i've woken up in a cold sweat with visions of this page in front of me. i especially like the "known physical data since 1860" part. not to mention the part about excluding gravity--since that would just be too much to ask!

link to nightmarish equation