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KOÇ UNIVERSITY PHYSICS SEMINAR
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Speaker : Ali Mostafazadeh, Koç University
Title : Geometric Extension of Quantum Mechanics
Date : October 2, 2018
Time : 14:30
Cookie & Tea : SCI 103 14:15
Place : SCI 103
web : https://physics-seminars.ku.
Abstract:
The search for a geometric generalization of Quantum Mechanics (QM) is usually motivated by the desire to formulate a consistent physical theory that would reduce to quantum mechanics and general relativity in different limits. There have been various attempts to generalize QM during the past 70 or so years, but it would be fair to say that no major progress could so far be made. The main source of the difficulty of this problem is the stringent and inflexible nature of the axioms of QM and the lack of experimental guidance towards their possible alternatives. In this talk I will propose a moderate geometric extension of QM that arises as a natural reaction to a simple no-go theorem for quantum systems with dynamical state spaces and elucidates the notion of “energy observable” for such systems. In the proposed theory, the role of the Hilbert space and the Hamiltonian operator is played by a complex Hermitian vector bundle E endowed with a metric-compatible connection and a global section of a real vector bundle determined by E. The axioms of QM are not replaced by others but elevated to the level of the relevant bundles. The talk will involve a rather extensive introductory part in which the basic structure of QM as well as the necessary mathematical tools will be reviewed. It will then focus on the conceptual aspects of the subject and their consequences.
Reference: A. M., Phys. Rev. D 98, 046022 (2018)
Short Bio: Ali Mostafazadeh was born in 1965 in Tabriz, Iran. He received his BS degrees in physics and mathematics from Boğaziçi University in 1989 and his Ph.D. in physics from the University of Texas at Austin in 1994 (under the supervision of Bryce DeWitt.). He held a Killam Postdoctoral position at the University of Alberta before joining Koç University in 1997. His areas of interest include geometric and topological aspects of quantum mechanics, supersymmetry and its generalizations, quantum cosmology, non-Hermitian operators, mathematical optics, and scattering theory. He is the author of 3 books and over 130 research publications, an elected principal member of the Turkish Academy of Sciences since 2007, and a recipient of TÜBİTAK Science Award the same year.