I have a question that I didn't see covered in any book that I read in QFT (I read so far Srednicki which I finished and Peskin and Schroeder which I haven't finished), can the vacuum generate an infinite number of real particles? How do we generate real particles from virtual particles? Is there such a process in QFT? I know that usually virtual particles are a mathematical tool, but then again also point particle is a mathematical tool. Thanks.