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 edit
- Shale, David (1962). "Linear Symmetries of Free Boson Fields". Transactions of the American Mathematical Society. 103 (1): 149–167. doi:10.2307/1993745. JSTOR 1993745.
- Shale, David (1962). "A Note on the Scattering of Boson Fields". Journal of Mathematical Physics. 3 (5): 915–921. Bibcode:1962JMP.....3..915S. doi:10.1063/1.1724306.
- Shale, David; Stinespring, W. Forrest (1964). "States of the Clifford Algebra". The Annals of Mathematics. 80 (2): 365. doi:10.2307/1970397. JSTOR 1970397.
- Shale, David; Stinespring, W. Forrest (1965). "Spinor Representations of Infinite Orthogonal Groups". Journal of Mathematics and Mechanics. 14 (2): 315–322. JSTOR 24901279.
- Shale, David (1966). "Invariant Integration over the Infinite Dimensional Orthogonal Group and Related Spaces". Transactions of the American Mathematical Society. 124 (1): 148–157. doi:10.2307/1994441. JSTOR 1994441.
- Shale, David; Stinespring, W. Forrest (1966). "Integration over Non-Euclidean Geometries of Infinite Dimension". Journal of Mathematics and Mechanics. 16 (2): 135–146. JSTOR 24901475.
- Shale, David; Stinespring, W. Forrest (1966). "Continuously splittable distributions in Hilbert space". Illinois Journal of Mathematics. 10 (4): 574–578. doi:10.1215/ijm/1256054896. ISSN 0019-2082.
- Shale, David; Stinespring, W. Forrest (1967). "The quantum harmonic oscillator with hyperbolic phase space" (PDF). Journal of Functional Analysis. 1 (4): 492–502. doi:10.1016/0022-1236(67)90013-4. Archived from the original (PDF) on 2019-03-24. Retrieved 2019-09-28.
- Shale, David; Stinespring, W. Forrest (1968). "Wiener processes" (PDF). Journal of Functional Analysis. 2 (4): 378–394. doi:10.1016/0022-1236(68)90002-5. Archived from the original (PDF) on 2019-04-15. Retrieved 2019-09-28.
- Shale, David; Stinespring, W. Forrest (1970). "Wiener processes II" (PDF). Journal of Functional Analysis. 5 (3): 334–353. doi:10.1016/0022-1236(70)90013-3.
- Shale, David (1973). "Absolute continuity of Wiener processes". Journal of Functional Analysis. 12 (3): 321–334. doi:10.1016/0022-1236(73)90083-9.
- Shale, David (1974). "Analysis over Discrete spaces". Journal of Functional Analysis. 16 (3): 258–288. doi:10.1016/0022-1236(74)90074-3.
- Shale, David (1979). "On geometric ideas which lie at the foundation of quantum theory". Advances in Mathematics. 32 (3): 175–203. doi:10.1016/0001-8708(79)90041-0.
- Shale, David (1979). "Random functions of Poisson type". Journal of Functional Analysis. 33: 1–35. doi:10.1016/0022-1236(79)90015-6.
- Shale, David (1982). "Discrete quantum theory". Foundations of Physics. 12 (7): 661–687. Bibcode:1982FoPh...12..661S. doi:10.1007/BF00729805. S2CID 119764527.
References edit
- ^ a b c d "In Memoriam, David W. H. Shale 1932–2016". Department of Mathematics, University of Pennsylvania.
- ^ 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.
- ^ David Winston Howard Shale at the Mathematics Genealogy Project
- ^ 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)