David Shale

David Winston Howard Shale (22 March 1932, New Zealand – 7 January 2016) was a New Zealand-American mathematician, specializing in the mathematical foundations of quantum physics. He is known as one of the namesakes of the Segal–Shale-Weil representation.

After secondary and undergraduate education in New Zealand, Shale became a graduate student in mathematics at the University of Chicago and received his Ph.D. there in 1960. His thesis On certain groups of operators on Hilbert space was written under the supervision of Irving Segal. Shale became an assistant professor at the University of California, Berkeley and then became in 1964 a professor at the University of Pennsylvania, where he continued teaching until his retirement.

"He was an expert in the mathematical foundations of Quantum Physics with many very original ideas on the subject. In addition, he discovered what is now called the Shale-Weil Representation in operator theory. He was also an expert in Bayesian Probability Theory, especially as it applied to Physics."

According to Irving Segal: "... although contrary to common intuitive belief, Lorentz-invariance in itself is materially insufficient to characterize the vacuum for any free field (this remarkable fact is due to David Shale; it should perhaps be emphasized that this lack of uniqueness holds even in such a simple case as the conventional scalar meson field ...), none of the Lorentz-invariant states other than the conventional vacuum is consistent with the postulate of the positivity of the energy, when suitably and simply formulated."