 Alan Weinstein

Alan Weinstein studies the mathematical interface between classical mechanics and quantum mechanics, particularly symplectic geometry. His Berkeley research profile identifies this connection.^[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.^[ref]

Alan Weinstein is likely a reference to an accomplished mathematician and physicist known for his work in areas such as mathematics, theoretical physics, and particularly in relation to symplectic geometry.