The Mobius symmetry of quantum mechanics.

3:00pm - 4:00pm / Wednesday 2nd December 2015
Type: Seminar / Category: Research
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Speaker: Prof. A.Faraggi (University of Liverpool)
Abstract: Phase space duality, manifested by the involutive
characteristic of Legendre transformations, and the equivalence
postulate of quantum mechanics, reveal that classical mechanics must
be modified by quantum mechanics. Underlying the formalism there
exist a cocycle condition and a basic quadratic identity, which are
invariant under D-dimensional Mobius transformations. The formalism
may be considered as adaptation of classical Hamilton-Jacobi theory
to quantum mechanics, yielding a quantum Hamilton-Jacobi equation
(QHJE). Energy quantisation arises in the formalism due to its
symmetry properties, without assuming the probability interpretation
f the wave-function, and predicts that spatial space is compact. It
is shown that time parameterisation of trajectories cannot follow
from its prevailing definitions in the literature, implying that
a trajectory representation does not exist in the QHJT. The formalism
provides a natural setting for the formulation of quantum gravity.
Evidence for the compactness of the universe may exist in
the CMB radiation.