### Quantum Field… Finance?

#### by Danielle Fong

One morning around the graduate college dining hall, there was a gathering of physicists, finance students, and economists. The physicists are always quite amazed by those people who decide to forgo the life of the ivory tower, and choose to strike out into the real world, and so could not be kept from asking what the economists actually did. Furthermore, we could not be kept from wondering aloud what type of mathematical models they built and polished, and whether any of them had a physical interpretation.

One of the economists scratched his head, drew a sip of black coffee from his porcelain cup, and mumbled something about how a large proportion of the physics department of Harvard University was hired by a trading company, with the lure of riches beyond the pale of the meager imaginings of the physicists (“you mean I can afford a house?!”).

But what did they do? Why them? What did the trading company see in them? I offered, from my experience in TopCoder, that trading companies appear to be mostly interested in hiring people who were very smart, and that maybe physicists at Harvard fit the bill.

“Uhmmm, no, not quite. I think it was something along the lines of specific expertise… something about, quantum… quantum field theory, maybe?”

I closed my eyes. Quantum field theory — gads! They’re going to use that for economics? Renormalization, Feynman diagrams, antimatter. I was aghast, finance would certainly be *fun* this way, but how on earth would anyone *use* it?

As my incredulity faded, it dawned on me. “Aha!” I exclaimed, “I think I know what they do! In Quantum Field Theory each normal mode oscillation of the field is interpreted as a particle, and all of these oscillations, coupled together, form the field. But we can just as well interpret an economic ‘price function’ as a field, and interpret each individual market player as a linear oscillator! The mathematics is exactly the same, so we can use *all* of the methods of QFT! It’s brilliant!”

I asked my friend across the table: “You must tell me. Did it actually work?”. He shook his head. “I don’t know. All of the results would be lost to the company. Perhaps if the stock rose inordinately it might say something, but how or why it happened would always be a mystery.”

Dejectedly, I pondered this. For perhaps the ex-physicists are happy, with their six-figure salaries and shiny urban lifestyles. But if I was them, well, I doubt I’d be able to handle keeping my application secret. And so I discovered yet another reason why I can’t live in the real world. I’m an intellectual show-off.

Michael Nielsen writes in to point out that Jim Simons, of Chern-Simon’s theory, is in fact the founder of Renaissance Technologies, a prominent hedge fund.

Presumably you’ve learned a ton about the connections since 2008, but one very amusing read about the connections is http://arxiv.org/abs/hep-th/9710148 , “The Physics of Finance”.

Hi Danielle,

Is this story real? Or is it totally made up…

I am asking because I have heard before that it is not uncommon for hedge funds to use advanced theoretical physics with the goal of predicting market behavior.

By the way, this is a very interesting blog. Great job!

It’s real