David Shale Explained

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. 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]

According to Irving Segal:

Selected publications

• 10.2307/1993745. 1993745. Linear Symmetries of Free Boson Fields. Transactions of the American Mathematical Society. 103. 1. 149–167. 1962. Shale. David. free.
• 10.1063/1.1724306. A Note on the Scattering of Boson Fields. Journal of Mathematical Physics. 3. 5. 915–921. 1962. Shale. David. 1962JMP.....3..915S .
• 10.2307/1970397. 1970397. States of the Clifford Algebra. The Annals of Mathematics. 80. 2. 365. 1964. Shale. David. Stinespring. W. Forrest.
• 24901279. Spinor Representations of Infinite Orthogonal Groups. Journal of Mathematics and Mechanics. 14. 2. 315–322. Shale. David. Stinespring. W. Forrest. 1965.
• 10.2307/1994441. 1994441. Invariant Integration over the Infinite Dimensional Orthogonal Group and Related Spaces. Transactions of the American Mathematical Society. 124. 1. 148–157. 1966. Shale. David. free.
• 24901475. Integration over Non-Euclidean Geometries of Infinite Dimension. Journal of Mathematics and Mechanics. 16. 2. 135–146. Shale. David. Stinespring. W. Forrest. 1966.
• Shale. David. Stinespring. W. Forrest. Continuously splittable distributions in Hilbert space. Illinois Journal of Mathematics. 10. 4. 1966. 574–578. 0019-2082. 10.1215/ijm/1256054896. free.
• Shale. David. Stinespring. W. Forrest. The quantum harmonic oscillator with hyperbolic phase space. Journal of Functional Analysis. 1967. 1. 4. 492–502. 10.1016/0022-1236(67)90013-4. free. 2019-09-28. 2019-03-24. https://web.archive.org/web/20190324111814/https://core.ac.uk/download/pdf/82034895.pdf. dead.
• Shale. David. Stinespring. W. Forrest. Wiener processes. Journal of Functional Analysis. 2. 4. 1968. 378–394. 10.1016/0022-1236(68)90002-5. free. 2019-09-28. 2019-04-15. https://web.archive.org/web/20190415184245/https://core.ac.uk/download/pdf/81122888.pdf. dead.
• Shale. David. Stinespring. W. Forrest. Wiener processes II. Journal of Functional Analysis. 5. 3. 1970. 334–353. 10.1016/0022-1236(70)90013-3. free.
• 10.1016/0022-1236(73)90083-9. Absolute continuity of Wiener processes. Journal of Functional Analysis. 12. 3. 321–334. 1973. Shale. David.
• 10.1016/0022-1236(74)90074-3. Analysis over Discrete spaces. Journal of Functional Analysis. 16. 3. 258–288. 1974. Shale. David.
• 10.1016/0001-8708(79)90041-0. On geometric ideas which lie at the foundation of quantum theory. Advances in Mathematics. 32. 3. 175–203. 1979. Shale. David.
• 10.1016/0022-1236(79)90015-6. Random functions of Poisson type. Journal of Functional Analysis. 33. 1–35. 1979. Shale. David. free.
• 10.1007/BF00729805. Discrete quantum theory. Foundations of Physics. 12. 7. 661–687. 1982. Shale. David. 1982FoPh...12..661S . 119764527.

References

1. Web site: In Memoriam, David W. H. Shale 1932–2016. Department of Mathematics, University of Pennsylvania.
2. 10.2307/2034661. 2034661. Some Remarks on Symplectic Automorphisms. Proceedings of the American Mathematical Society. 16. 3. 393–397. 1965. MacKey. George W.. free.