Career
He helped establish the phase space formulation of quantum mechanics in 1949 by bringing together the ideas of Hermann Weyl, John von Neumann, Eugene Wigner, and Hip Groenewold. This formulation is statistical in nature and makes logical connections between quantum mechanics and classical statistical mechanics, enabling a natural comparison between the two formulations. "Phase Space Quantization," is a synonym for "Moyal Quantization" and largely avoids use of operators for quantum mechanical observables prevalent in the canonical formulation.
Quantum-mechanical evolution in phase space is specified by a Moyal bracket.
Moyal grew up in Tel Aviv, and attended the Herzliya Hebrew Gymnasium. He studied in Paris in the 1930s, at the École Supérieure d"Electricité, Institut de Statistique, and, finally, at the Institut Henri Poincaré.
His work was carried out in wartime England in the 1940s, while employed at the de Havilland Aircraft company.