Kenneth G. Wilson Quotes

You shouldn’t choose a problem on the basis of the tool. You start by thinking about the physics problem, and the computational method should be a tool like any other. Maybe you’ll solve it using computer techniques, maybe using a contour integral; but it’s very important to approach it starting from the physics because otherwise you get lost in the use of the tool, and lose track of where you’re trying to go.

The fourth aspect of renormalization group theory is the construction of nondiagrammatic renormalization group transformations, which are then solved numerically, usually using a digital computer. This is the most exciting aspect of the renormalization group, the part of the theory that makes it possible to solve problems which are unreachable by s. The Kondo problem has been solved by a nondiagrammatic computer method.

Asymptotic freedom arises as follows. The fundamental interactions of quarks and gluons are modified by “radiative” corrections of higher order in the quark-gluon coupling constant. These radiative corrections depend on the quark and gluon momenta. A careful analysis shows that the cumulative effect of radiative corrections to all orders can be characterized by a momentum-dependent effective coupling constant. The effective coupling is found to vanish in the limit of large momenta (to be precise, large momentum transfers between the quarks and gluons). This is called asymptotic freedom. As a result of asymptotic freedom the quarks can behave as nearly free particles at short distances; this is required to explain the high energy electron scattering experiments ... Meanwhile the interactions of quarks at long distances can be strong enough to bind the quarks into the observed bound states; protons, mesons, etc.

Sometime toward the end of my second year, I started working with Gell-Mann. I went to Gell-Mann and he gave me a problem to work on and suggested I start working with fixed source theory of K-particles, where he wanted me to do things involving strong and weak interactions. And it's when I read about fixed source theory that I began to learn about renormalization group and realized it could be applied to fixed source theory, and I don't know whether there were papers that I read about renormalization group and fixed source theory, or I worked it out for myself, but in playing around with this, sort of trying to learn what was going on, I discovered that there were great simplifications that took place when you took the fixed source equation and took them to high energies, and when you did a leading log approximation. In the end, I discovered that those equations, simplified at the high energies -- you could get exact solutions. That was part of my thesis. And that was the initial thing that sparked my interest in the renormalization group. I remember when I presented my thesis to a seminar, and this was when Feynman was there, but not Gell-Mann. I went through all this exciting mathematics and toward the end, someone said, "Yes, that's fine, but what good is it?" I remember Feynman's answer as "Don't look a gift horse in the mouth!"

An especially intractable breed of problems in physics involves those with very many or an infinite number of degrees of freedom and in addition involve “renormalization.” Renormalization is explained as the existence of very many length or energy scales of importance in the physics of the problem. The renormalization group approach is a way of reducing the complexity of these problems to the point where numerical methods can be used to solve them. The Kondo problem (dilute magnetic alloys) is used as an illustration.