I am trying to write a statement of purpose for a PhD position in physics in the UK. I have a master’s degree in physics which is the standard requirement for such a position. I have been interested in this subfield for a long time, have read many papers about it, taken all of the relevant undergrad courses, and my dissertation was also in this general area.
I have mentioned all of this in my SOP, but the problem is that because the subfield is highly technical, I know basically nothing about the actual position I am applying to. I picked several of the (hundreds of) potentially relevant papers I could find, and spent the last week trying to work through them, but any one of these papers would probably take months for me to understand in any detail. It is not that I lack the educational background for this position, rather that it is just a very specific project in an unfamiliar topic.
I’m concerned that if I just make vague comments about why the potential impact of the group’s research is exciting, it will look like I haven’t bothered to even try to understand their work. On the other hand, being overly specific seems risky given that I know almost nothing about their research.
A complication is that I applied for a (different) PhD project with the same group last year, and received an offer which I then turned down.
Based on the 10% of what I have read that I could actually understand, the topic of the position I am applying for seems exactly like something I would enjoy, and I want to try to make it clear that I am very serious about wanting to work with this group, and have at least made an effort to understand what the project entails. But I don't want to seem like I'm bluffing, or arrogantly overstating my level of knowledge. It might even be possible to apply without saying anything specific about the project at all, but to compensate for weaker aspects of my application, and the fact that I previously decided against working with this group, I want to emphasise my interest in this specific position.
Is there any general guidance (preferably specifically for physics/mathematics) about how to discuss your motivation to work on a project you do not understand? While I am in the UK, I would appreciate advice based on other countries as well.