Understanding QFT

( This is a draft. ) Big up to my boy David Tong for his notes on this topic.

Any experience with high school electricity and magnetism will tell you that it is treated differently than Newtonian mechanics. We are introduced to the idea of a field. At the same time, we are told that the electron is a player in the field. In introductory E&M, electrons and photons sometimes appear as particles in their own classical right, but other times they are treated as ripples in the EM field. In the quantum world, electorns and photons are treated on equal footing. The question stands, should we take the particle or the field as fundamental? The hypothesis of QFT is that the field comes first. Particles are the ripples in the fundamental structure that is the field. Experiencing and growing up with classical objects like billiard balls and tables and phones, we are not accustomed to thinking of reality as a field. So this exercise will be quite time and energy consuming. But hang on.

Why QFT?

First of all, we do we even need QFt, are we not happy with just talking about chairs and tables and phones as objects in their own right? Well, this view worked for a long time and it is still a useful tool for understanding the world. But, some strange phenomena occurs in the world around us that cannot be explained by considering objects as particles. For example, the sun exerts a force at a distance on us earthlings, taking us along the joyride of the cosmos. Light bends arounda a corner, interferes with itself and in some places, acts really weirdly (See the double slit experiment). Because the combinaton of special relativity and quantum mechanics implies that particle number is not conserved. First discoverd by Dirac with the introduction of the positron. Particles are created and destoryed and ephemeral.

No Mas

Consider a mass trapped in a box of size $L$. Heisenberg tells us that the uncertainty in the momentum $\Delta p \geq \frac{\hbar}{2L}$. Uncertainty in the energy is on the order of $\Delta E \geq \frac{\hbar c}{2L}$. When the uncertainty exceeds $\Delta E = 2mc^2$, particle anti-particle virtual pairs pop out of the vacuum. So if mass m is localized in a box of size $L = \hbar/4mc$. Length is called the Compton wavelength, at which point the concept of a particle breaks down.

Virtual particles are not measurable by an experiment, hence the name. So they can violate the laws of physics if they are not measurable, seems very convenient.

Why are there no errors in the proton production and a proton from a cosmic ray and one from a accelerator are identical.