Physics dissertation: Do I give a reference every time I mention a certain piece of work?

Yes indeed. For several reasons:

• people might not read your work sequentially, from page 1 to the end;

• people might forget that there was already a citation somewhere;

• people don't want to recall all previous citations;

• the context is different and people don't assume that the reference is the same.

The short answer is yes, for the reasons mentioned by Massimo Ortolano.

How sparsely can you cite? If you're talking about others' work, you should make it clear what work you're talking about at least once a paragraph. E.g.:

The Planck Collaboration ([1]) produced estimates of cosmological constants using lasers and mirrors. The lasers were really cool and allowed them to precisely measure X as equaling pi. Further, Y was e, and Planck's constant was 7.

It also turns out that Z is a complex number, 1+7i. This further implies that our universe is shaped like a donut. The implications go further, suggesting time is periodic. [1]

Having the citation at the end of the paragraph means that every single fact in that paragraph is sourced from that paper. If you are interspersing your own calculations or implications, then you would have to put the citations back at the sentence-by-sentence level.

If your work is in conversation with one main work, then you may have a case for giving them a nickname for that section only, instead of constantly citing them.

In this section that follows, I closely review the 2012 paper by the Planck Consortium [1]; for convenience, I will refer to that work as PC.

...

PC further found that Z is complex. I question that assumption based on my calculations. If we start with PC's assumption of ..., then necessarily ...