Hans A. Kastrup

Hans A. Kastrup (2019)

Hans A. Kastrup (born July 4, 1934 in Bielefeld ) is a German physicist and professor emeritus for theoretical physics with a research focus on particle physics ( symmetries and field theories ), astrophysics ( black holes ), fundamentals of quantum theory ( quantization of classical systems, Wigner functions ) and history and philosophy (philosophy of science ) of physics and mathematics.

Short academic biography

Kastrup was a student at the Helmholtz grammar school in Bielefeld from 1946 to 1955 , where he received special support from the director Heinrich Rüping. He then completed a degree in physics at the Ludwig Maximilians University of Munich (LMU), supported by the German National Academic Foundation . In May 1962 his doctorate at LMU followed with a dissertation on possible applications of conformal transformations in particle physics (reviewer: Fritz Bopp and Werner Heisenberg ). From 1962 he was a research assistant at the Institute for Theoretical Physics (Chair F. Bopp). In July 1964 he completed his habilitation at the LMU with the thesis “Consequences of the dilatation group in very high energies” (reviewers also Fritz Bopp and Werner Heisenberg).

In 1964 and 1965, Kastrup conducted research on a Volkswagen Foundation grant at the Lawrence Radiation Laboratory in Berkeley, California . He then worked at the invitation of Eugene Wigner as a research associate at the Palmer Physical Laboratory of Princeton University (Wigner had mentioned one of Kastrup's first publications in his 1963 Nobel Prize in Physics). From 1966–1967 he taught at the invitation of Heinrich Leutwyler as a visiting professor at the Institute for Theoretical Physics at the University of Bern and from 1967 to 1972 he was Scientific Counselor and Professor at the Institute for Theoretical Physics at the University of Munich.

From 1964 to 1972, Kastrup and co-workers mainly researched the application of conformal transformations of the Minkowski space to high-energy scattering processes in particle physics, in particular to the asymptotic behavior of relativistic amplitudes , in which masses in the momentum space are negligible for the associated four- momentum pulses .

In 1972 Kastrup was appointed to the newly established chair for elementary particle physics in the Institute for Theoretical Physics at RWTH Aachen University and was appointed one of the directors of the institute. The research area Theoretical Elementary Particle Physics was established in the institute in the following years and expanded with two further professorships and additional staff positions.

Kastrup's numerous graduate and doctoral students include the later professors Gerhard Mack ( University of Hamburg ), Mario Dal Cin ( University of Erlangen ), Karl Blum ( University of Münster ), Dieter H. Mayer ( University of Clausthal-Zellerfeld ), Thomas Mohaupt ( University of Liverpool ) , Thomas Thiemann (University of Erlangen), Martin Bojowald ( Pennsylvania State University , Pennsylvania, USA).

After his retirement from RWTH Aachen University in 1999, Kastrup was an invited guest scientist at the European research center CERN near Geneva for one year and has been a guest scientist at the DESY research center in Hamburg since 2001 at the invitation of the theory group .

Kastrup was married twice: from 1964 to 1989 with Barbara Lee, b. Jonas. The marriage had four children: Martin, David, Philipp and Bettina. From 1992 to 2018 he was with Dorothea, geb. Göttsche († 2018), married.

research

A large part of Kastrup's publications is characterized by the application of group theoretical methods to the description of different physical systems and their symmetries .

After passing the pre-diploma examination, Kastrup began in the summer of 1959, as a student at the chair for theoretical physics at LMU Munich, to familiarize himself with modern topics in elementary particle physics. The chair holder Fritz Bopp was Arnold Sommerfeld's successor and had dealt with non-local classical field theories , the fundamentals of quantum mechanics as well as symmetries of physical systems including the associated mathematical symmetry groups.

The Max Planck Institute for Physics , which moved to Munich in 1958 and under its director Werner Heisenberg, had a formative influence on Kastrup, and with its well-known scientists and numerous lectures it provided decisive suggestions. This also included the course lecture " Quantum Mechanics " given by Heisenberg at the LMU in SS 1959 .

Inspired by the application of scale transformations ( dilatations ) in Heisenberg's (physically and mathematically inadequate) nonlinear spinor theory and by a work by Bopp on the conformal invariance of Maxwell's equations , Kastrup began with the 15-parametric conformal group of the Minkowski space as a generalization of the 10-parametric inhomogeneous Lorentz Group to deal with in detail. A conceptual difficulty with the topic was that the physically contradicting interpretation of the 4-parametric subgroup of special conformal transformations of the Minkowski space as a transformation from an inertial to an accelerated system, which had prevailed for decades, had brought this subgroup into disrepute as physically unusable . Instead, Kastrup interpreted these conformal transformations as space-time-dependent scale transformations (gauge transformations of Minkowski space) in his dissertation . This interpretation, which prevailed in the following years, led to an abundance of publications on applications of conformal transformations in relativistic quantum field theory (with short distances or with such large impulses that masses are negligible) and in the statistical mechanics of phase transitions , especially those caused by the early ones important work by his doctoral student Gerhard Mack (since 1967)

The renewed general interest in classical field theories , especially gauge theories , stimulated Kastrup after 1974 to deal with canonical structures of classical field theories, which can be characterized by Lagrange functions and which had been examined in their diversity primarily by the Belgian mathematician Théophile Lepage

As part of a working group at the chair, Kastrup was involved in analyzing quantum field theories on grids, especially the Higgs model and its phase transitions .

Via the group-theoretical quantization of phase spaces , Kastrup came to the problem of the quantum theory of black holes and their thermodynamics , based on the identification of binary degrees of freedom of the elementary (surface) quanta of black holes as the geometric quantity orientation .

The emerging ambiguities of string theories , along with a lack of physical predictions, led Kastrup to pursue Ashtekar's approach to quantizing gravity, which led to the influential dissertations and international careers of his doctoral students Thomas Thiemann and Martin Bojowald in this field.

Kastrup's latest work deals with the group-theoretical quantization of the canonical quantity angle by means of the trigonometric functions sin and cos. This also resulted in a consistent definition of Wigner functions for the canonical pair angle and orbital angular momentum with an infinite cylinder as phase space , including possible applications in quantum information .

Review article (selection)

• Canonical Theories of Dynamical Systems in Physics , Physics Reports, Vol. 101 (1983) pp. 1-167; doi .
• The Contributions of Emmy Noether, Felix Klein and Sophus Lie to the Modern Concept of Symmetries in Physical Systems , extended version of the lecture, given during the conference SYMMETRIES IN PHYSICS (1600–1980), 20–26 Sep 1983, St. Feliu de Guixols , Spain , Proceedings editors: MG Doncel, A. Herrmann, L. Michel, A. Pais; Barcelona, ​​Spain, Servei de Publications, Barcelona Autonoma U., 1987, 678pp. Here pp. 113-164;
• Quantization of the canonically conjugate pair angle and orbital angular momentum , Physical Review A73 (2006) 052104; doi ; e-Print: quant-ph / 0510234.
• A new look at the quantum mechanics of the harmonic oscillator , Annalen der Physik (Berlin), Vol. 16 (2007), pp. 439-528; doi ; e-Print: quant-ph / 0612032
• On the advancements of conformal transformations and their associated symmetries in geometry and theoretical physics , Annalen der Physik (Berlin), Vol. 17 (2008), No. 9-10, pp. 631-90; doi ; e-Print: arXiv: 0808.2730 [physics.hist-ph]

Web link

• Homepage
• Literature by and about Hans A. Kastrup in the catalog of the German National Library
• Directory of most publications on Inspire, an information system for particle physics

Individual evidence

1. ↑ Hans Kastrup, Obituary for Fritz Bopp , Physikalische Blätter, Vol. 44 (1988), Heft 3, pp. 77-78; doi .
2. ↑ Details on the history of conformity invariance in mathematics and physics can be found in the review article V.
3. ^ HA Kastrup: On the physical interpretation and representation-theoretical analysis of the conformal transformations of space and time , Annalen der Physik, 7th part (Leipzig), Vol. 9 (1962), pp. 388-428; doi . Text is available on Kastrup's DESY homepage .
4. ^ HA Kastrup: Gauge Properties of the Minkowski space , Phys. Review, Vol. 150 (1966), pp. 1183-1193; doi .
5. ↑ See chap. 6 u. 7 in the review article V.
6. ↑ See the review article I.
7. ^ HA Kastrup, Schwarzschild black hole quantum statistics from Z (2) orientation degrees of freedom and its relations to Ising droplet nucleation , Annalen der Physik (Berlin). Vol. 9 (2000), pp. 503-522; doi ; e-Print: gr-qc / 9906104
8. ↑ See the review article III.
9. ^ HA Kastrup, Wigner functions for the pair angle and orbital angular momentum , Phys. Rev. A94 (2016) 062113; doi ; e-Print: arXiv: 1601.02520 [quant-ph].