Hi, 

with_user(user) function return a new version of this record set attached to the given user,
in non-superuser mode, unless `user` is the superuser (by convention, the superuser is always in superuser mode.

In your code,

public_user = self.env.ref('base.public_user')
public_book = self.env['library.book'].with_user(public_user)

Regards