Bucknell Physics 212 Supplement

Section 10.3 Quantum Field Theory

Modern physical theory seeks to explain all four of the fundamental interactions — gravity, electromagnetism, strong, and weak — in terms of quantum fields. Here's how classical models explain how two particles exert forces on one another: each particle sets up a field that the other particle reacts to, and these fields obey certain equations (like Faraday's Law). This, of course, isn't really an explanation at all, because it doesn't really explain what a field is and why one particle should produce a field and why another particle should respond to this field.

In quantum field theory, the fields themselves are quantized; changes in the fields occur in discrete lumps. The lumps of energy and momentum can be considered particles, often called messenger particles. As an analogy, think of two people playing catch. The ball passes back and forth between the players and transmits the exchange of momentum and energy.

Let's see how this works for electric forces. The quantum field theory for electromagnetic interactions is called quantum electrodynamics or QED. In this theory an electrically charged particle — an electron, for instance — makes its presence known not by setting up an electric field, but by continually emitting and absorbing electromagnetic messenger particles, or photons. Because these photons are not detected as particles of light, but serve only to transmit energy and momentum between particles, they are also called virtual photons. In fact, at any given time, an electron is literally surrounded by a cloud of these virtual photons, appearing and disappearing.

Where does the energy come from to create all these photons? Doesn't energy have to be conserved? The answer is that short-term violations of the law of conservation of energy are permitted by the quantum uncertainty relations, as we have already seen in tunneling. The uncertainty relation for time and energy, analogous to \(\Delta x\, \Delta p \geq \hbar/2\text{,}\) is

In effect, (10.1) permits particles to borrow an amount of energy \(\Delta E\) from the surrounding space so long as the energy is returned within a time \(\Delta t \approx \hbar/\Delta E\text{.}\) In this view, even empty space itself is loaded with activity, as virtual particles and messengers pop into existence and then quickly disappear!¹

Current theory holds that there are messenger particles like photons that act as the intermediaries for all of the fundamental interactions. For the weak interaction, they are the massive (as in, having mass) vector bosons \(W^+\text{,}\) \(W^-\text{,}\) and \(Z^0\text{.}\) For the strong interaction, they are the colored gluons, which act between quarks. The properties of the messenger particles are listed in Table 10.1. You'll learn more about these messenger particles in this and the next chapter. In addition, a particle called the graviton is postulated as the messenger for gravity.