**Friday, February 9, 2007**

Finite Quantum Theory

**Mohsen Shiri **

Harvard and Pace Universities

The three main revolutions of physics in the twentieth century have a suggestive family resemblance. Each of them introduces a certain non-commutativity previously not present in physics. Special relativity introduces a non-commutativity of boosts. General relativity introduces a non-commutativity of infinitesimal translations. Quantum theory introduces a non-commutativity of observations (measurements). The seminal works by Segal and Inönün and Wigner suggest more changes of this kind. Most major changes in physical theories are examples of a process we term *group regularization *. We regularize the usual quantum theory to a finite quantum theory by deforming the Heisenberg group and test the new theory on quantum harmonic oscillator. The finite harmonic oscillator is now a quantum rotator with its momentum and positions as bounded operators with discrete spectrum, much like the angular momentum operators of the usual quantum rotator. The resulting finite quantum theory is a crucial step toward developing a quantum theory of spacetime (gravity.)

Refreshments at 4:00 PM. Seminar begins at 4:10 PM.

Building 8 (Science Bldg.) - Room 241

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