= Alan Weinstein
{c}
<Alan Weinstein> studies the mathematical interface between <classical mechanics> and <quantum mechanics>, particularly <symplectic geometry>. His Berkeley research profile identifies this connection.https://vcresearch.berkeley.edu/faculty/alan-d-weinstein[Institutional research statement]{ref}
With <Sean Bates>, he wrote <Lectures on the Geometry of Quantization by Sean Bates and Alan Weinstein>. Their treatment of <half-densities> explains how to integrate products of wave-like objects intrinsically: the product of two half-densities is a density, giving a coordinate-independent inner product and hence a <Hilbert space>. This is part of the geometric infrastructure needed to relate classical phase spaces to quantum states.<Lectures on the Geometry of Quantization by Sean Bates and Alan Weinstein>[Preface and Appendix A, pp. 119–121]{ref}
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