His 1946 thesis paper laid the foundations of quantum mechanics in phase space, in unwitting parallel with J. E. Moyal. This treatise was the first to achieve full understanding of the Wigner–Weyl transform as an invertible transform, rather than as an unsatisfactory quantization rule. Significantly, this work further formulated and first appreciated the all-important star-product, the cornerstone of this formulation of the theory, ironically often also associated with Moyal's name, even though it is not featured in Moyal's papers and was not fully understood by Moyal.