Regular Transformation Homework: Definition & Interpretation

[gotjrgkr]

Homework Statement

Hi!
i want to ask somebody who are studying quantum mechanics about the definition of regular
transformation. I guess there might be people who are not familiar with the notion. So, i'd like to let you know which book I'm referring to; "principles of quantum mechanics" , shankar.
In sec.2.7,2.8 of the book, the concept of regular transformation is introduced (more precisely please, refer to p. 97-p.98). It describes the notion of regular transformation with two other concepts passive trans. and active trans. . It says if we restrict the range of functions transforming points from a phase space to another one to those functions preserving the ranges of the domain and the range of each function, we say such functions(or transformation ) as regular transformation.
What I want to know is whether such a transformation (regular trans.) involves passive transformation or not . Does it only imply active transformation? or is it also possible to be interpreted as passive transformation? For those people who think the latter is also possible, how can you interpret the words written in p. 103 ? You can find a sentence " but, it is an active transformation" in the third line from the bottom. I thought the word " it " there implies regular transformation. However, considering the whole stories back and forth of the page 103, I expect that the meaning of "it" there must be interpreted as "the problem".
In fact, I'm not a native speaker. I have a difficulty to interpret some sentences. I'm really sorry to ask you about this trivial stuff, but I thought that if I pass this part ignoring those concepts, then I expect I'm going to misunderstand lots of concepts following the chapter2 (especially, those parts of the book dealing with conservation, symmetry in chatper 11,12)
So, please help me. I would really appreciate your helps. Thank you for reading my long questions!

Homework Equations

The Attempt at a Solution

 

[member 553083]

A regular transformation is one that preserves the ranges of the domain and range of each function. This means that it does not involve any passive transformations, but only active transformations. The sentence "but, it is an active transformation" on page 103 is referring to the regular transformation, as it is the only type of transformation mentioned in the context of the sentence.