# Contents

## Idea

There are at least two formalizations of quantization, one of them is geometric quantization. In this context a quantum state is identified with a certain section (a polarized section) of a certain complex line bundle: the prequantum line bundle.

Here a section of the prequantum line bundle is what is physics is called a wave function or probability amplitude on the space of field configurations. A choice of polarization on this space is a choice of “canonical coordinates” and “canonical momenta”. Hence a polarized section, and hence a quantum state in the sense of geometric quantization, is, in physics language, a wave function of the canonical coordinates.

For details see at geometric quantization – Space of quantum states.

duality between algebra and geometry in physics:

holographic principle in quantum field theory

bulk field theoryboundary field theory
dimension $n+1$dimension $n$
fieldsource
wave functioncorrelation function
space of quantum statesconformal blocks

Revised on July 17, 2013 23:33:56 by Urs Schreiber (82.169.65.155)