Preface to the Special Issue dedicated to Prof. Heller

Preface to the Special Issue dedicated to Prof. Heller Demonstr. Math. 2017; 1: 1–1Demonstratio MathematicaOpen AccessEditorialLeszek Pysiak* and Wiesław SasinPreface to the Special Issuededicated to Prof. HellerDOI 10.1515/dema-2017-0001Received November 16, 2016; accepted November 16, 2016.Michał Kazimierz Heller was born on 12 March 1936 in Tarnów. He holds a chair of philosophy at the PontificalUniversity of John Paul II in Cracow, Poland, and is an adjunct member of the Vatican Observatory. He is amember of Pontifical Academy of Science. His current research is concerned with the singularity problem in generalrelativity and the application of noncommutative geometry to physics and cosmology, in particular in seeking theunification of general relativity and quantum mechanics. In 2008 he was awarded the Templeton Prize for ProgressTowards Research or Discoveries about Spiritual Realities in appreciation of his dedication at understanding andexplaining the interaction of science and religion. He is a Roman Catholic priest and mathematical cosmologist whochampiones a word view that combines mathematical physics, theology and philosophy. He is the recipient of anhonorary degree from Warsaw University of Technology. Since 1987 he cooperates with the group of mathematiciansfrom the Differential Geometry Department of the Warsaw University of Technology. His influence on this groupwas paramount. Seminars of the group took place in Warsaw and in Cracow interchangeably. Summer and winterseminars were organized in Pasierbiec near Limanowa. The concept of differentiable manifold remains crucial inmodelling many physical phenomena. In particular, space-times of all major physical theories are supposed to havethe structure of a sufficiently smooth manifold. However, in some areas of research there is a necessity to go beyondthis assumption and to consider some generalizations. At the beginning of the cooperation Prof. Heller got an ideato use differential space concept in the sense of Sikorski in order to construct a generalized model of space-timewhich would possibly contain also classical space-time singularities. The first summer school ’Differential Spacesand Their Applications’ took place in Pasierbiec, 20-26 September 1990. The special issue of the ’DemonstratioMathematica’ Vol XXIV No 3-4 (1991), contains works presented at this school. In the next period the group wasengaged in works concerning a theory of the groupoid model unifying general relativity and quantum mechanics.The group used methods of the noncommutative geometry and considered the convolution algebra of functions onthe transformation groupoid over the total space of frame bundle of the space-time with the action of the Lorentzgroup. They constructed the differential geometry, based on derivation of the algebra end considered the generalizedEinstein's equation as the eigenvalue equation for the Einstein operator. Next they investigated the quantum sectorof the model representing the algebra in a bundle of Hilbert spaces and obtaining a von Neumann algebra of randomoperators. This algebra allowed to define the dynamics of random operators by Tomita-Takesaki theorem and todefine a noncommutative probability measure (in the sense of Voiculescu's probability theory). It was the idea ofProf. Heller to seek a mathematical structure rich enough to be suitable approximated by the mathematical structuresof general relativity and quantum mechanics. The influence of Professor Michał Heller on the group was invaluable.The present issue is dedicated to Prof. Michał Heller in honor of his eightieth birthday.*Corresponding Author: Leszek Pysiak: Faculty of Mathematics and Information Science, Warsaw University of Technology,Koszykowa 75, 00-662 Warszawa, Poland, E-mail: l.pysiak@mini.pw.edu.plWiesław Sasin: Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00-662 Warszawa,Poland, E-mail: w.sasin@mini.pw.edu.pl© 2017 Pysiak and Sasin, published by De Gruyter Open.This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

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© 2017 Leszek Pysiak and Wiesław Sasin
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Abstract

Demonstr. Math. 2017; 1: 1–1Demonstratio MathematicaOpen AccessEditorialLeszek Pysiak* and Wiesław SasinPreface to the Special Issuededicated to Prof. HellerDOI 10.1515/dema-2017-0001Received November 16, 2016; accepted November 16, 2016.Michał Kazimierz Heller was born on 12 March 1936 in Tarnów. He holds a chair of philosophy at the PontificalUniversity of John Paul II in Cracow, Poland, and is an adjunct member of the Vatican Observatory. He is amember of Pontifical Academy of Science. His current research is concerned with the singularity problem in generalrelativity and the application of noncommutative geometry to physics and cosmology, in particular in seeking theunification of general relativity and quantum mechanics. In 2008 he was awarded the Templeton Prize for ProgressTowards Research or Discoveries about Spiritual Realities in appreciation of his dedication at understanding andexplaining the interaction of science and religion. He is a Roman Catholic priest and mathematical cosmologist whochampiones a word view that combines mathematical physics, theology and philosophy. He is the recipient of anhonorary degree from Warsaw University of Technology. Since 1987 he cooperates with the group of mathematiciansfrom the Differential Geometry Department of the Warsaw University of Technology. His influence on this groupwas paramount. Seminars of the group took place in Warsaw and in Cracow interchangeably. Summer and winterseminars were organized in Pasierbiec near Limanowa. The concept of differentiable manifold remains crucial inmodelling many physical phenomena. In particular, space-times of all major physical theories are supposed to havethe structure of a sufficiently smooth manifold. However, in some areas of research there is a necessity to go beyondthis assumption and to consider some generalizations. At the beginning of the cooperation Prof. Heller got an ideato use differential space concept in the sense of Sikorski in order to construct a generalized model of space-timewhich would possibly contain also classical space-time singularities. The first summer school ’Differential Spacesand Their Applications’ took place in Pasierbiec, 20-26 September 1990. The special issue of the ’DemonstratioMathematica’ Vol XXIV No 3-4 (1991), contains works presented at this school. In the next period the group wasengaged in works concerning a theory of the groupoid model unifying general relativity and quantum mechanics.The group used methods of the noncommutative geometry and considered the convolution algebra of functions onthe transformation groupoid over the total space of frame bundle of the space-time with the action of the Lorentzgroup. They constructed the differential geometry, based on derivation of the algebra end considered the generalizedEinstein's equation as the eigenvalue equation for the Einstein operator. Next they investigated the quantum sectorof the model representing the algebra in a bundle of Hilbert spaces and obtaining a von Neumann algebra of randomoperators. This algebra allowed to define the dynamics of random operators by Tomita-Takesaki theorem and todefine a noncommutative probability measure (in the sense of Voiculescu's probability theory). It was the idea ofProf. Heller to seek a mathematical structure rich enough to be suitable approximated by the mathematical structuresof general relativity and quantum mechanics. The influence of Professor Michał Heller on the group was invaluable.The present issue is dedicated to Prof. Michał Heller in honor of his eightieth birthday.*Corresponding Author: Leszek Pysiak: Faculty of Mathematics and Information Science, Warsaw University of Technology,Koszykowa 75, 00-662 Warszawa, Poland, E-mail: l.pysiak@mini.pw.edu.plWiesław Sasin: Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00-662 Warszawa,Poland, E-mail: w.sasin@mini.pw.edu.pl© 2017 Pysiak and Sasin, published by De Gruyter Open.This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.

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Demonstratio Mathematicade Gruyter

Published: Apr 25, 2017

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