I have swamped you with a lot of methods, being the important tools I use for research. The natural question is: What do I do with them?
Well, this changes over time. This is quite normal. If you do research, you do not know what lies ahead. As you make progress, things you know change. This may be due to you own research, or by results from other people's research. Some topics may become less interesting as they appeared some time ago. Others become more interesting, and more relevant. This is a slow, but continuous evolution. It is the normal way things go: The most important characteristic of research is that you never know in advance where it will take you. Only when you get there, you will finally know.
Thus, what I will describe now and in the next few entries, is not set in stone. It is, what I am currently working on. In fact, when I started this blog, I was only investigating the standard model. And within it, I was mostly concentrating on the strong interactions, QCD. That was some time ago. By now, the topics I am looking at have became somewhat broader. I have also started to look at topics which are more mathematical, and also at some which are beyond the standard model. Anyway, I will not change the title of the blog: What today is beyond the standard model may be the standard model of tomorrow, you never know. I will also, from time to time, give you an update, when a new topic becomes interesting.
Let me now concentrate on the topics of my current research. I will list them in an order which is not indicating importance. It is rather my, somewhat subjective, view from what is well-founded to what is more speculative.
The first topic is the most mathematical one. As you remember, local symmetries are very important in the standard model. As any new standard model will contain the standard model as a special case, so will local symmetries continue to play an important role. These symmetries have been recognized to be important in particle physics already before the 1940s. At first sight, one may expect that everything is known about them, what there is to know. However, the combination of local symmetry and quantization is very complicated. It becomes especially problematic when you look at an interaction like QCD, which is very strong and complex. For many purposes, we have this problems under control. We can calculate what happens in QCD when we can use perturbation theory. We can also deal with the local symmetry when we calculate something like the proton mass. But in both cases, this more operational then a full solution. Beyond this, things become very complicated, as I will discuss in the next entry.
The second topic is QCD. QCD is a very rich topic, and just saying QCD is not very specific. Let me be more specific. One of nowadays great challenges in QCD is to understand what happens if we have many, many quarks and gluons. In this case, they may be a very dense, and possibly hot, soup. Describing this soup is dubbed 'determining the phase diagram of QCD'. This phase diagram is of great importance. Such a soup is expected to have existed in the early universe. It likely exist today within the core of neutron stars. Thus, in this topic elementary particle physics meets with astrophysics. I will discuss this in detail later.
The third topic is about the Higgs. Or rather about the interplay between the weak force and the Higgs. I am not really interested in what they actually precisely measure at the LHC. At least, not yet. Right now, I am trying to understand some rather basic questions about Higgs physics. These are closely related to the fundamental questions I am working on about local symmetries. However, just recently, this may actually lead to some predictions about what the may measure. You will see more about this in an upcoming entry.
The last topic is rather speculative. I try to understand what may be there beyond the standard model. Right now, we have few hints what may be the next big thing after the standard model. Thus, you are rather free in your speculation. Again, I am more interested in how the things, whatever they are, may function. Nonetheless, I have to be somewhat specific at least about the rough shape of the topic I am considering. Right now, I am most interested in what is called technicolor. I will explain this scenario (and other ideas for beyond-the-standard-model physics) in an upcoming entry. For now, it suffices to say that it has both local symmetry and strong interactions. This makes it rather messy, and therefore interesting. Let me give you the details later, in another entry.
As you see, I am interested in a number of rather different questions. But there is a common theme to all of them. What I want to understand is the mix of local symmetry and strong interactions. What does this mix imply for the physics? What is going on with these two concepts in the standard model, and beyond? How can we mathematically deal with these theories? Do we really understand what they mean? And what possibilities does this combination hold, once we get a full and firm grip on it? These are the questions I want to know the answers to. These are the things which may shake up what we know. Or, they may be just fixing some minor detail in the end. What of both will be the case, I cannot say yet. I will only know it, when I understood it. And to follow these questions is very interesting, very fascinating, and, yes, very exciting. I am very curious about where my research leads me. Let me take you along for the ride.