My Life as a Quant by Emanuel Derman

local gauge invariance.
    The standard model related nature’s forces to each other much like Mendeleyev’s periodic table had connected the diverse chemical elements. Mendeleyev had detected a hint of order in the properties of elements and then deduced the existence of other as yet-undiscovered elements necessary to complete the pattern. Similarly, Glashow, Weinberg, and Salam had detected a pattern in both the weak and electromagnetic forces, and then deduced the existence of other previously undiscovered weak forces necessary to complete their picture. The sum total of all these forces comprised the standard model. It was an ambitious but compelling theory; when it was verified, its creators won the Nobel Prize. Much of theoretical particle physics works in this way: You hear a few isolated bars of a beautiful song and try to figure out the whole piece by generalizing the pattern in the fragments.
    My thesis work over the next three years employed both the theory of quarks and the Weinberg-Salam standard model which predicted new weak forces between electrons and quarks. One of these new forces, the so-called weak neutral current , would cause a small violation of parity in the collisions of electrons and quarks. If protons were bags of quarks, one should also be able to observe a small violation of parity in electron-proton collisions. The effect would be small and subtle, for the most part masked by the much stronger electromagnetic force between electrons and quarks.
    In my thesis I proposed a new test of the standard model. In particular I suggested that experimentalists at SLAC try to observe the effects of the standard model’s parity-violating weak force in the inelastic collisions of electrons with protons. In order to estimate the size of the signal, I made use of many of the skills I had gained during the past few years. I employed Lee and Yang’s framework for analyzing parity violation and I used Feynman’s parton-model description of the proton as a bag of quarks. In this way I calculated how much of a parity-violating asymmetry would be seen if the standard model were indeed correct.
    I began my research in 1970. Slowly, I read the multitude of papers that explained how to use the parton model, repeating their published calculations on my own and checking that I could reproduce their results. Step by step, I learned the mechanics of the model and how to use it. Then I began my own work.
    My first task was to carry out the long mathematical calculations that predicted the distribution of electrons recoiling after a collision with a quark. I did each calculation using “Feynman diagrams,” the cartoon-like representation invented by Feynman to systematize the ways in which particles interacted during collisions. I drew all the possible diagrams that could occur in a theory, and then, using Feynman’s rules, translated each picture into a mathematical formula and evaluated it. The calculations, carried out with pen and paper, took up tens of pages. I repeated each calculation at least twice to check for consistency. When successive calculations didn’t match, I searched each one for errors and eliminated them until I found agreement. Today, however, much of the repetitive algebraic manipulation would be done with symbolic mathematical programs like Mathematica™.
    Feynman’s diagrams and rules were a sort of bookkeeping-by-picture process that miraculously captured all the details of the standard model in a series of diagrams; they allowed people less talented than Feynman to perform the most complex calculations carefully and correctly. Many of the great advances in physics are like this; they codify and make routine what was formerly almost impossible to think about. Whenever I have a new problem to work on—in physics or options theory—the first major struggle is to gain some intuition about how to proceed; the second struggle is to transform this intuition