Characterization of non-polynomial Bopp-shiftable expressions

Determine a general class of non-polynomial expressions that admit useful Bopp-shift evaluations, and establish their relevance in actual quantum theories, to support the implementation of corresponding specialized algorithms in SymQuPS.

Background

SymQuPS evaluates quantum phase-space star products primarily through Bopp shifts, with polynomial expressions receiving explicit algorithmic treatment. The appendix illustrates that some non-polynomial expressions, such as f(α,α*) = e^α, also permit a Bopp-shift evaluation.

The paper states that the authors have not identified a general class of non-polynomial expressions with this property or determined whether such expressions are relevant to actual theories. Consequently, SymQuPS does not currently implement specialized algorithms for these cases, leaving their systematic characterization and practical significance unresolved.