Quantum Theory for Mathematicians pp 483-526 | Cite as

# Geometric Quantization on Manifolds

## Abstract

Geometric quantization is a type of *quantization*, which is a general term for a procedure that associates a quantum system with a given classical system. In practical terms, if one is trying to deduce what sort of quantum system should model a given physical phenomenon, one often begins by observing the classical limit of the system. Electromagnetic radiation, for example, is describable on a macroscopic scale by Maxwell’s equations. On a finer scale, quantum effects (photons) become important. How should one determine the correct *quantum* theory of electromagnetism? It seems that the only reasonable way to proceed is to “quantize” Maxwell’s equations—and then to compare the resulting quantum system to experiment.

### Keywords

Manifold Electromagnetism### References

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