Can Noncommutative Operators Be Integrated in Quantum Mechanics?

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SUMMARY

The discussion centers on the integration of noncommutative operators within Quantum Mechanics (QM), specifically addressing the expression [A,B]=iħ1. The participants explore the feasibility of defining a noncommutative integral, represented as ∫ dA dB exp(-iAB), where A and B are operators. The consensus indicates that traditional integration methods in QM do not typically accommodate operator integration, raising questions about the definition of a 'measure' dA for operators.

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mhill
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since in QM we deal with noncommutative operators , for example

[tex][A,B]=i\hbar 1[/tex]

then my question is if we could define some kind of noncommutative integral

[tex]\int dA dB exp(-iAB)[/tex] here A and B would be operators

how can you define for an operator a 'measure' [tex]dA[/tex]
 
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In general one never integrates over operators in QM.
 

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