From Harmonic Oscillators to Quantum Gravity

par John Klauder (University of Florida)

mercredi 19 mai 2021, 14:00 → 15:00 Europe/Paris

https://greenlight.lal.cloud.math.cnrs.fr/b/fab-49u-gkt

Canonical quantization (CQ) has been successful in solving many problems, and is a tool used for nearly all cases. But CQ has not worked well for some problems that have resisted any acceptable solution. Happily, the harmonic oscillator, with -∞ < p,q < ∞, is well solved. However, for the half-harmonic oscillator, where -∞ < p < ∞ while 0 < q < ∞ CQ fails significantly. Likewise, quantum gravity has failed with CQ as well. A new quantization process called affine quantization (AQ) will be introduced. AQ leads to acceptable solutions for the half-harmonic oscillator and shows considerable success for quantum gravity. This lecture will demonstrate the solution of the half-harmonic oscillator and leads to a meaningful Schrödinger equation for quantum gravity, which is in position to seek appropriate solutions from complex differential equations.