BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Edwin Beggs (Swansea University) DTSTART:20200610T111500Z DTEND:20200610T121500Z DTSTAMP:20260423T010753Z UID:MatPhySem/5 DESCRIPTION:Title: Quantum geodesics in quantum mechanics\nby Edwin Beggs (Swansea Univ ersity) as part of Mathematical Physics Seminar\n\n\nAbstract\nWe show tha t the standard Heisenberg algebra of quantum mechanics admits a noncommuta tive differential calculus $Ω^1$ depending on the Hamiltonian $H=p^2/2m+V (x)$ and a flat quantum connection with torsion on it such that a quantum formulation of autoparallel curves (or `geodesics') reduces to Schrödinge r's equation. The connection is compatible with a natural quantum symplect ic structure and associated generalised quantum metric. A remnant of our a pproach also works on any symplectic manifold where\, by extending the cal culus\, we can encode any hamiltonian flow as `geodesics' for a certain co nnection with torsion which is moreover compatible with an extended symple ctic structure. Thus we formulate ordinary quantum mechanics in a way that more resembles gravity rather than the more well-studied idea of formulat ing geometry in a more quantum manner. We then apply the same approach to the Klein Gordon equation on Minkowski space with a background electromagn etic field\, formulating quantum `geodesics' on the relevant relativistic Heisenberg algebra. Examples include a proper time relativistic free parti cle wave packet and a hydrogen-like atom. based on a joint work with Shahn Majid.\n LOCATION:https://researchseminars.org/talk/MatPhySem/5/ END:VEVENT END:VCALENDAR