TL;DR
This paper explores the relationship between regular pseudo-bosons and ordinary bosons, analyzing their mathematical properties and the role of intertwining operators, to clarify their similarities and differences.
Contribution
It provides a detailed comparison between regular pseudo-bosons and bosons, including the role of bounded and unbounded intertwining operators, expanding understanding of their mathematical structure.
Findings
Regular pseudo-bosons are closely related to bosons through specific intertwining operators.
Bounded and unbounded intertwining operators play different roles in the pseudo-bosons framework.
The analysis clarifies the mathematical distinctions and connections between pseudo-bosons and bosons.
Abstract
We discuss in which sense the so-called {\em regular pseudo-bosons}, recently introduced by Trifonov and analyzed in some details by the author, are related to ordinary bosons. We repeat the same analysis also for {\em pseudo-bosons}, and we analyze the role played by certain intertwining operators, which may be bounded or not.
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