When I get asked what I do, I usually give a top-down answer and stop whenever I detect boredom in my victims' eyes. If you are signed up for more and more, keep clicking!
I am a PhD candidate at the University of Bonn. I do theoretical particle physics (more accurately - phenomenology) in the group of Bastian Kubis and Christoph Hanhart.
[I am also signed up as a Master's student in computer science, but that's a whole other story.]
We work with hadrons, which are composite particles. You might know some of the elementary particles, like electrons, photons, etc. Hadrons are (gross oversimplification coming) states made up from quarks and gluons, held together by the strong interaction. There are hundreds of them known to mankind, documented by the Particle Data Group. Famous examples are:
- Baryons, such as
- Protons (made up using 2 up quarks and 1 down quark),
- Neutrons (1 up quark and 2 down quarks),
- etc...
- Mesons, such as
- Pions (up and down quarks),
- Kaons (strange quarks),
- etc...
I work with mesons, especially, with the pions, which are the lightest of them. My task is to study the connection of the pions with the electromagnetic current (=a fancy name for a photon). This inevitably means that I am interested in electrons/positrons and photons as well, since most pions we study are produced in electron-positron collisions.
We use dispersion relations and here is why. What we care about are two basic principles: unitarity and analyticity.
Unitarity is connected with something called "probability conservation". This may sound complicated, but it really means a simple thing. In quantum mechanics, we work with an object called a "wavefunction". The wavefunction (squared) gives a probability distribution. The requirement for any probability distribution is that the area below the curve is equal to 1. In simple terms, this means that the total probability is 1 (or 100%). By time, the wavefunction of a physical state changes. But the resulting wavefunction must also produce a probability distribution. A mathematician's way of saying this is that time evolution must be a unitary operation ("unit" = 1), otherwise (as sloppier physicists usually say) "probability is not conserved".
When we say analyticity, we mean the properties of the scattering amplitude as a function on the complex energy plane. The reason why we care if this function is analytic is that this ensures a very important principle - causality, that is the future should not affect the past. Strictly speaking, scattering matrix is not analytic, but meromorphic, which means that certain singularities are allowed, but there is always a physical reason behind them. For instance, branch cuts are associated with the production of particles, poles with resonances, etc. When we compare our models with the experimental data, we only have access to the absolute value of the scattering matrix in isolated regions of the complex plane. The information about the rest of the plane comes from analyticity.
If we are dealing with a meromorphic (analytic up to singularities) function, we can use the Cauchy's integral formula to analytically continue the function from the real axis to the whole complex plane, integrating over the singularities. This is the essence of dispersion relations.
I do, how dare you!
On a more serious note: it depends... If you want to immediately see the results of your research affect millions of lives on Earth, yes - there are more applied fields than theoretical particle physics. That being said, I do think that everyone should care about fundamental research. It took the borderline obsessive curiousity of past scientists to get us to the point of knowing electromagnetic radiation so well that we can develop the technology we all see today. There is no way of knowing if we will ever use pions (i.e. what I study) the same way as we use protons and neutrons, but you never know until you look deep inside. There should always be people caring about the laws of nature, even if their application is centuries away.