How to protect your authorship when trapped in "collaboration"? Some time ago, my advisor has put me working together with some group colleagues on a very loosely defined theoretical physics project. From the beginning, I didn't like this too much because I felt that what was planned to be done, I could do by myself, and I felt the other students were added to the project just to help my advisor have less work and distribute responsibility to the other group members. I also felt from the beginning these students were not very friendly and collaborative because they displayed either lack of interest by my project, jealousy, or an attitude of dispute.

During this time, I have had novel and significant ideas by myself, which are already enough to write a paper with; these people have contributed almost no meaningful insights. Essentially, they worked on the same things I worked on after I had shown them (hence just providing a redundancy check), and are now helping in writing the paper and interpreting what I found out (but I could also do that)...

Furthermore, as this is my project, they are not pushing to advance it that much, and it gets worse because I feel that sometimes, out of jealousy maybe, they even push me down and try to diminish my ideas in front of my advisor without actually providing reasonable arguments for why they don't like some of my approaches... etc...

This is the context, now comes my question.

I managed to really advance this project as I gradually became more and more passionate about it. The paper we are preparing already introduces important and novel results (again, that I alone obtained). But just now I had a eureka moment and improved what we were doing (and writing) once more; with this new result, it becomes much more significant... I'm feeling I can make an important contribution to my field: a new method, with theoretical guarantees, proofs... I did this during the last week and haven't shown them yet. My dilemma is: should I disclose the new results already and publish those in the paper we are preparing or should I keep this and prepare a new one?

Again, I've been doing all of this by myself but "officially" we are in this together, which is what is pushing me back to consider these questions. It would make much more sense to add this new result to the present paper and not spread ideas in multiple publications, but even though I am the first author, it feels to me that others are getting credit for work they didn't do/contributed to. These were entirely my ideas. If someday people refer to this result/theorem as the ABCD result, with initials or something, it seems very unfair to me, as I discovered this entirely by myself. I am planning to ask my advisor these questions but I'd like to hear other takes on the problem. If this turns out to be really important, how can I manage to keep the credit for my method if I disclose it in a paper with other collaborators? Will I be able to also put these results in my Ph.D. thesis and safely be recognized as its single author?
how can I...keep the credit for my method if I disclose it in a paper with other collaborators? 


You can't: Credit will be shared between all collaborators.*


  Will I be able to also put these results in my Ph.D. thesis and safely
  be recognized as its single author?


Yes.

*In some sense, you can get credit, since the result appears in your thesis, which suggests that you are primarily responsible for results. But, your published paper is more likely to be considered the primary source of the results. (I suppose you could submit your thesis before publishing the paper, or you could release a preliminary draft of your thesis before publishing, then you could cite your thesis/draft thesis in the published paper, which may give you slightly more public credit.)


  should I disclose the new results already and publish those in the paper we are preparing or should I keep this and prepare a new one?


This seems likely to produce opinion-based answers, which are off-topic here.