I'm searching for a concrete definition of operation and method independent of the programming language.
In my understanding:
Operations just specify which functionality an object supports without any implementation. It seems to be like a prototype in a C header.
Methods specify the concrete implementations an object supports. It seems to be like an implemented C function.
Question:
Why do we speak of abstract methods? In my opinion abstract methods should be the same like operations.
Searching pascal.computer.org for operation gives numerous and varied definitions. In the context of this question, the second seems most fitting.
in programming, a defined action that can be performed by a computer system
That definition sounds vague in isolation, but ties nicely into the definition of method.
implementation of an operation
...which is exactly as stated in the question. However, I think these formal definitions differ from colloquial usage. The term operation is somewhat rare in OOP. I would use it in the context of a mathematical operation, especially as the action of a mathematical operator, but not as a substitute for a method definition. Abstract method would be a more common phrase in that case.
Likewise, while method is a quintessential OOP term, it is not typically used to call out an implementation. Concrete method would be the inverse of abstract method. I think the lesson is that while academic definitions exist, programmers don't necessarily speak that way. This is no different to common conversation diverging from the dictionary.
See also: What's the difference between a method and a function?
