Squeezing: the ups and downs

Abstract: We present an operator theoretic side of the story of squeezed states regardless the order of squeezing. For low order, that is for displacement (order 1) and squeeze (order 2) operators, we bring back to consciousness what is know or rather what has to be known by making the exposition as exhaustive as possible. For the order 2 (squeeze) we propose an interesting model of the Segal-Bargmann type. For higher order the impossibility of squeezing in the traditional sense is proved rigorously. Nevertheless what we offer is the state-of-the-art concerning the topic.