When physicists want to tame the beast of infinities, they use the powerful theoretical machineries of renormalization. Gerard ‘t Hooft vividly and lucidly described these fundamental ideas in his Nobel Lecture dated December 8, 1999. According to him, there are two approaches toward renormalization: mass and charge.

For mass renormalization, we need to imagine that a particle such as an electron is like a tiny sphere, of radius R and bare mass M and since it possesses electric charge Q, its energy derived from the electric field is

[math]E=\frac{Q^2}{8\pi R}[/math]

However, according to Einstein’s special relativity, this gives a mass excess of [math]E/c^2[/math] Therefore the true physical mass of the electron is now

[math]M_T=M+\frac{Q^2}{8\pi c^2 R}[/math]

It is this physical mass that can be measured when using Newton’s 2nd law of motion. Nevertheless, infinity begins its unruliness when R approaches the value of zero, which sends the value of the mass correction term to infinity.

For charge renormalization, we need to consider the charge correction from the effect of vacuum polarization. This effect screens or disguises the bare charge of an elementary particle giving a lesser value for its experimentally measurable electric charge. Similarly, as R approaches zero, the excess energy term tends toward infinity.