Symbol Correspondence for Euclidean Systems
In this dissertation, we construct the star-product or ?-product of functions on the Euclidean motion group E(n), n = 2, 3 by way of the twisted convolution formulated on E(n). The construction is motivated by the theorem that connects the Weyl quanti- zation and the Wigner function given by hWσf|gi...
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| Format: | text |
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Archīum Ateneo
2019
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| Online Access: | https://archium.ateneo.edu/theses-dissertations/448 |
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| Institution: | Ateneo De Manila University |
| Summary: | In this dissertation, we construct the star-product or ?-product of functions on the Euclidean motion group E(n), n = 2, 3 by way of the twisted convolution formulated on E(n). The construction is motivated by the theorem that connects the Weyl quanti- zation and the Wigner function given by hWσf|gi = (2π) −n/2 Z Rn Z Rn σ(x, ξ)WG(f, g)dxdξ, where Wσ is the Weyl quantization associated with σ in the Schwartz class, S (R n ), and WG(f, g) is the Wigner function of f, g ∈ S (R n ). The objects Wσ and WG(f, g) are constructed by means of the unitary irreducible representations of E(n). We will also show the properties of Wigner functions, as well as the ?-product of functions on E(n), and establish their relationship. The objects Wσ, WG and ? are three of the main objects of the formalism of quantum mechanics in phase space. |
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