So you want to add an imaginary scientific discipline or two into your science fiction or fantasy story. It might be necessary for you as an author, and not all of the material will be incorporated into the story. Or, you actually need that set for any particular character you are developing. Anyway, it’s a part of worldbuilding.
You can outline the discipline in brief or give it a more deep and detailed sketch—whatever the story needs, and go have some brainy fun.
What your notes on imaginary sciences (as well as the professions, vocations and intellectual pursuits—don’t forget that science is done by people/other intelligent entities*) should include?
Here’s a list of the elements you’ll need to put some thought into:
1. A methodological introduction — a justification of desirability of a particular science discipline, its subject and method; of possibilities for its practical application and use.
2. Define a place of this scientific discipline among a number of other disciplines — existing and/or imaginary.
3. Development of a categorical apparatus of science, the introduction of relevant terms and their relationships.
4. As rigorous as possible definitions of these terms, including different interpretations of those by any of the possible scientific schools.
5. A brief illustration — excerpts from the alleged writings on a particular subject. Quoted text(s) may be imaginary (as is your new scientific discipline) — but they must be appropriate to the nature and objectives of the discipline in question and demonstrate its categorical apparatus in action.
6. A brief (or not) characteristics of general position in science, its main achievements, contradictions, unresolved problems, creative perspectives, as well as the main characteristics of schools, trends and directions of the science – in their struggle, controversy, etc.
7. Recommendatory bibliography — with a brief description and evaluation of the most noteworthy and fundamental research, that somehow prepares (prepared—yes, history!) the creation of this science.
* Here’s further food for thought on this one: Know Your Characters’ Skill Sets