prof. Stern's seminar at SISSA

[Emanuele Tuillier Illingworth]

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MATHEMATICAL PHYSICS SECTOR SEMINARS
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Allen Stern (Tuscaloosa, USA)

"Properties of Snyder space"

Wednesday 15 June, 16:00, room 136 (SISSA, Santorio Building, I floor)


Abstract:
Although the Snyder algebra was written down over 60 years ago,
remarkably, its consequences have not yet been fully understood.
Here we examine the subalgebra generated by the spatial  coordinates
and momenta and show that it has two distinct infinite dimensional
representations.  Both are spanned by  spherical harmonics defined
on one hemisphere of S3.  They correspond the position operator having
either an integer or half-integer spectrum and yield two distinct
spatial lattices. The lattices are consistent with the continuous
symmetries of space-time.  Two  different approaches can be taken
to introducing particle dynamics on these lattices.  In the more
conservative approach, one holds on to the traditional interpretation
of time as a real parameter associated with the evolution of the
system. However, then consistency demands that the Hamiltonian is
deformed, thereby leading to non standard energy-momentum dispersion
relations.
On the other hand, one can retain the conventional energy-momentum
dispersion relation if one adapts a more radical view, where  time
corresponds to  the spectra   of some  noncommuting operator.
The introduction of such a time operator has interesting consequences
for kinematics on the lattice.