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Symplectic and Lagrangian polar duality; applications to quantum harmonic analysis

Polar duality is a well-known concept from convex geometry and analysis. In the present paper we study a symplectically covariant versions of polar duality, having in mind their applications to… Click to show full abstract

Polar duality is a well-known concept from convex geometry and analysis. In the present paper we study a symplectically covariant versions of polar duality, having in mind their applications to quantum harmonic analysis. It makes use of the standard symplectic form on phase space and allows a precise study of the covariance matrix of a density operator.

Keywords: applications quantum; polar duality; quantum harmonic; harmonic analysis; duality

Journal Title: Journal of Mathematical Physics
Year Published: 2024

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