It applies for things that you are expected to have, and where it would be most natural that you would be speaking about your own one. Like jag borstar tänderna – not everyone has teeth, but there's an expectation that most people do, and that you would be most likely to brush your own teeth. In those contexts we don't say min/mitt/mina since it's so obvious, instead we just use the definite form.
Without context, people aren't expected to have their own book with them, so without more information than we have here, boken just means the book.
I came here to ask precisely this because I just had "Jag tar på mig skorna" where the definiteness of 'the shoes' is used instead of the possessiveness of "mina" (my) shoes to indicate that they belong to the person making the statement. That led me to believe that this sentence could mean that the book belongs to the person being asked the question.
Did you bring the book? was an accepted answer here by mistake, and I'm removing it now. That sentence should preferrably be translated into Swedish as Tog du med dig boken?
The thing is, those sentences might be used in the exact same context sometimes, but that doesn't mean they are good translations of each other in terms of this course.
It's a particle because med is always stressed, and reflexive because the reflexive pronoun changes with person:
jag har med mig
du har med dig
hon har med sig
vi har med oss
ni har med er
de har med sig
An interesting thing is that the order is different here, as compared to bryr sig om.
Remember that the reflexive pronoun must match the subject: it must be Har du boken med dig? and Tar du hatten av dig?
The latter is possible, but it sounds somewhat odd, I would definitely prefer Tar du av dig hatten? If you put hatten first, you stress that word very strongly, as if the context were: I really expected you to take your shoes off, but now you're taking your HAT off?
Fronting the thing you've brought in this way seems more natural to me than fronting the thing you are taking off, but Har du med dig boken? is still the default word order and Har du boken med dig? is more special.
Can someone please explain why doesn't this mean "Do you bring the book?". I was just introduced to this new verb, and then next question uses it but does not accept, even as an option, the previous meaning. I read all the answers but none of them really explain why. Tack för hjälpen!
I fully understand the examples you gave me, but still don't get why Duo didn't accept my answer. Basically in your examples you can use this sentence to refer to something that you already did (bring the book, or asking if you did) or something that will happen (ska ta). I will pretend though that I'm right thinking that "do you bring the book" is not accepted because of the present tense. I guess this is the kind of thing I'll look back to in some months from now and wonder what I did not understand at the time. I'm a native Spanish speaker and would be glad to help you if needed. Thanks for your help again!