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.^[1] He is known as one of the namesakes of the Segal–Shale-Weil representation.^[2]

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.^[1] His thesis On certain groups of operators on Hilbert space was written under the supervision of Irving Segal.^[3] 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.^[1]

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.^[1]

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.^[4]