- #1
andresB
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I studied the basics of geometric quantization for a recent work in quantum-classical hybrid systems1. It was an easy application of the method of gometric quantization (prequantization + polarization in ##\mathbb{R}^{3}##).
The whole topic seems interesting since I want to learn more of symplectic geometry, but (outside the aforementioned half-quantization to get a quantum-classical theory) I fail to see the point of the whole endeavor. For example, particles constrained to move on a surface are treated with the formalism of the geometric potential of Jensen, Koppe, and Da Costa2 , and not from a quantization of the related classical situation.
What actual result from geometric quantization is important and useful outside the mathematical dicipline of geometric quantization itself?[1]https://arxiv.org/abs/2107.03623
[2]https://arxiv.org/abs/1602.00528
The whole topic seems interesting since I want to learn more of symplectic geometry, but (outside the aforementioned half-quantization to get a quantum-classical theory) I fail to see the point of the whole endeavor. For example, particles constrained to move on a surface are treated with the formalism of the geometric potential of Jensen, Koppe, and Da Costa2 , and not from a quantization of the related classical situation.
What actual result from geometric quantization is important and useful outside the mathematical dicipline of geometric quantization itself?[1]https://arxiv.org/abs/2107.03623
[2]https://arxiv.org/abs/1602.00528
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