Quantizer–dequantizer operators as a tool for formulating the quantization procedure |
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Institution: | 1. Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991, Russia;2. Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow Region 141700, Russia;3. Russian Quantum Center, Skolkovo, Moscow 143025, Russia;4. Department of Physics, Tomsk State University, Tomsk 634050, Russia |
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Abstract: | We consider the quantization procedure and investigate the application of the quantizer–dequantizer method and star-product technique to construct associative products and the associative algebras formed by the quantizer–dequantizer operators and their symbols. The corresponding Lie algebras are also constructed. We study the case where the quantizer–dequantizer operators form a self-dual system and show that the structure constants of the Lie algebras satisfy some identity, in addition to the Jacobi identity. Using tomographic quantizer–dequantizer operators and their symbols, we construct the continuous associative algebra and the corresponding Lie algebra. |
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Keywords: | Associative algebras Lie algebras Star-product Quantizers Dequantizers |
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