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]

Selected publications

References

  1. 1 2 3 4 "In Memoriam, David W. H. Shale 1932–2016". Department of Mathematics, University of Pennsylvania.
  2. ↑ MacKey, George W. (1965). "Some Remarks on Symplectic Automorphisms". Proceedings of the American Mathematical Society. 16 (3): 393–397. doi:10.2307/2034661. JSTOR 2034661.
  3. ↑ David Winston Howard Shale at the Mathematics Genealogy Project
  4. ↑ Segal, I. E. (1962). "Mathematical characterization of the physical vacuum for a linear Bose-Einstein field". Illinois Journal of Mathematics. 6 (3): 500–523. doi:10.1215/ijm/1255632508. (quote from p. 501)
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