Download Or we may do physics

Possibly even right
Noncommutative Geometry
and the real world
According to some strings are not
even wrong
• They are at best a mathematical theory
without any possibly verifiable connection
with the real world
• Are we like them or can we be wrong?
• Can we be right?
• What do I mean by Noncommutative
Geometry?
Where do we come from?
• Quantum Mechanics (Heisenberg, Dirac,
Von Neumann Moyal)
• Mathematics (Gel’fand, Connes)
• Strings (Frohlich, Seiberg, Witten)
• Quantum Field Theory- Structure of space
time at Planck lenght (Doplicher,
Fredhenagen, Wess….)
Where can we go?
• Mathematics
• There have been lots of successes in
mathematics
• This is a noble activity, and apart that it
may create problems with funding
agencies I see nothing wrong in doing it
• Or we may do physics
Connes’ standard model
• It is nor really noncommutative, the
structure of spacetime is unchanged
• It makes predictions testable at LHC
Κ-Minkowski
• It is an Hopf Algebra with a rich structure
• It has non trivial dispersion relations
• They could help explain some
astronomical observations of γ ray burst
• The dispersion relations depend on the
basis!
Moyal Plane
• Consider θ as a background tensor
• Most of the effects are a consequance of
Lorentz non invariance
• Accelerator experiments (Trampetic, Ohl)
• Cosmology. Inflation makes a huge
amplification of short distance effects (up
to 10^13 GeV at Planck)
Θ-Poincaré
• We still have a (deformed) Lorentz
Invariance
• We can study deformations of Gravity (al
et Wess)
• Spin Statistics
Are we mature
enough to make
predictions?