Realization of associative products in terms of Moyal and tomographic symbols
A. Ibort, V. I. Man'ko, G. Marmo, A. Simoni, C. Stornaiolo, and F., Ventriglia
TL;DR
This paper explores how associative products can be realized within the quantizer-dequantizer framework, providing solutions in finite dimensions and examples in infinite dimensions.
Contribution
It demonstrates that any associative product can be realized via the quantizer-dequantizer method in finite dimensions and offers specific examples for infinite-dimensional cases.
Findings
Associative products can be realized through the quantizer-dequantizer approach in finite dimensions.
The paper provides explicit examples of such realizations in infinite-dimensional spaces.
The inverse problem has a positive solution in finite-dimensional settings.
Abstract
The quantizer-dequantizer method allows to construct associative products on any measure space. Here we consider an inverse problem: given an associative product is it possible to realize it within the quantizer-dequantizer framework? The answer is positive in finite dimensions and we give a few examples in infinite dimensions.
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