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Junior GST
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Jacob Gaiter, PMA 9.166: Deformation Quantization and Symmetry
Monday, September 19, 2022, 12:00pm - 01:00pm
In the early days of quantum mechanics, Dirac put forth that the proper way to quantize a classical system was to (in modern terms) replace the Lie-Poisson algebra of functions on phase space by a noncommutative algebra whereby Poisson brackets are replaced with a multiple of the commutator. In this talk we discuss the obstructions of Groenewold and Van Hove which prevent a quantization from satisfying Dirac's quantization prescription and the ideas of Bayen, Flato, Fronsdal, Lichnerowicz, and Sternheimer which allow us to circumvent the so-called no go theorems. If time permits, we will look at how to use symmetry to reduce the dimension of a classical system and a method for finding a corresponding reduction of the quantum observables.
Location: PMA 9.166

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