# nLab geometry of physics -- quantum mechanics

This is a sub-entry of geometry of physics.

# Contents

So far we have discussed extended prequantum field theory: Lagrangians and their induced action functionals and prequantum n-bundles. Now we turn to actual quantum field theory. A prequantum field theory is supposed to induce a quantum field theory under the last step of higher geometric quantization: a choice of polarization (or equivalent) and the passage to the corresponding space of states of polarized sections of the prequantum n-bundles. This step that connects prequantum field theory with quantum field theory we discuss below in Geometric Quantization.

Here we discuss the structure of the outcome of this process.

## Quantum mechanics

### Syntactic Layer

#### Directed homotopy type theory

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