He's just using it as a synonym for "Consider..." or "Assume we have...", which is a really common way to start. I didn't find this paper to read very differently from a contemporary paper in Physical Review Letters, except that there's no introduction that gives context within the rest of the literature.

Using the word "imagine" isn't that unusual. Here's some examples in just the past couples of years:

"We might then imagine other starting points which..."

"...let us now imagine that..."

"Let us imagine a potential of the form..."

https://scholar.google.com/scholar?as_ylo=2015&q=imagine&hl=...

To me it read more like a math text than a physics text, in which "let there be X...", "imagine Y...", and similar phrases, are usually found. Yet I agree, it seems the physics community has grown a slight alergy to that kind of writing, and it probably would be received with a bit of skpeticism/disdain nowadays.

Nothing special about the "imagine" portion; plenty of research in theoretical Computer Science takes an even more informal.approach in the introduction.